Stability Matrix Research Articles

Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems

Abstract Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment is the average rate at which phase space contracts. Here, we use this identity and the properties of a classical density matrix to derive upper and lower bounds on the entropy flow rate with the spectral properties of the local stability matrix. These bounds are an extension of more fundamental bounds on the Lyapunov exponents and phase space contraction rate of continuous-time dynamical systems. They are maximal and minimal rates of entropy production, heat transfer, and transport coefficients set by the underlying dynamics of the system and deterministic thermostat. Because these limits on the macroscopic dissipation derive from the density matrix and the local stability matrix, they are numerically computable from the molecular dynamics. As an illustration, we show that these bounds are on the electrical conductivity for a system of charged particles subject to an electric field.

Impulse synchronization strategy for supply chains considering combined effects and demand saturation

Supply chains often face sudden changes in production, distribution, and consumption as a result of factors such as pandemics, Black Friday, and mass production by manufacturers; this is called the ”impulse phenomenon.” The effect of the impulse phenomenon on the supply chain system can be positive or negative. Understanding how to use the impulse phenomenon to synchronize supply chain systems and avoid chaos is therefore important for supply chain management. Existing studies mainly use continuous synchronization strategies as a means to avoid chaos in supply chain systems; however, a discrete impulse synchronization strategy is easier to implement. Considering combined effects of consumption,distribution,production and demand saturation, this study constructs a supply chain system composed of a manufacturer, distributor, and retailer. We then construct a supply chain system with uncertain parameters and input disturbance. Using Lyapunov stability theory and matrix inequality, we obtain the impulse synchronization strategies of two supply chain systems. Finally, taking China’s supply chain system of corn, wheat, and rice as an example, we compare goodness of fit. The production, distribution, and consumption of rice are controlled using a temporary storage purchase policy, batch ordering, and promotion activities, and the effectiveness of the impulse synchronization strategy is verified. Our results show the following: (1) Considering combined effects and demand saturation, the supply chain system has better goodness of fit and better impulse synchronization. (2) When a chaotic supply chain system deviates from its expected state, if impulse intensity and the time interval satisfy Theorem 1 or 2, the supply chain system can be restored to its expected state; if not, the synchronization effect might not be achieved. (3) Generally, when impulse intensity is low, the time interval is short, if impulse intensity is high, the time interval should be longer.

Cognitive Model Based on The Dl Random Forest Method for Profi t Forecasting and Fuzzy Algorithm for Assessing Company Sustainability in Conditions of Uncertainty

The article is devoted to the problem of supporting management decision-making on choosing a strategic partner whose activities would be effective and sustainable. During the study, based on the results of the work of enterprises in the domestic confectionery industry, a dataset was generated, which was subsequently used for the deep learning model DL-model "Random Forest" in order to calculate the predicted values of the net profi t of enterprises in the industry. Assessing companies for the purpose of selecting a strategic partner, using models such as: deep learning model "Random Forest" (DL Random Forest), VaR, Z-Altman, Hurwitz matrix, Fuzzy algorithm in modern conditions has great practical significance. The relevance of the study lies in the fact that in conditions of increasing market uncertainty, approaches to ensuring the sustainable development of an organization based on AI systems are increasingly being used. The scientific novelty lies in the fact that the study used a set of models that made it possible to assess the actual sustainability of companies and, based on the calculated forecast values of net profi t, as well as business efficiency indicators ROE and ROS, to make a decision on the choice of potential business partners. During the study the following were developed: a VaR model, which made it possible to obtain an assessment of fi nancial risk, a Z-Altman model for assessing the risk of bankruptcy of an enterprise. In addition, based on the calculated parameters of the regression equation, a Hurwitz matrix was formed, which made it possible to draw a conclusion about the sustainability of each enterprise as a system. The use of the Fuzzy algorithm made it possible to obtain a decision on choosing a partner enterprise.

Binary nano-systems TiO2-ZnO and TiO2-Cu in the chitosan matrix: synthesis and photocatalytic properties

Abstract Binary TiO2-ZnO and TiO2 - nanoparticles (NPs) Cu in a chitosan stabilizer matrix were obtained and studied as photocatalysts at their content relative to the mass of the dry polymer of 10 wt.%. The effect of the mass ratio of TiO2:ZnO, TiO2:Cu NPs was revealed on the photocatalytic properties of materials in the decomposition reaction of methylene orange when exposed to UV and visible light. It is shown that the greatest depth of decomposition of the azo dye - 98% – in an aqueous solution is achieved in 60 minutes of light exposure using the system TiO2:ZnO with a mass ratio of 1:1 and 2:1 components. The same level of photocathaitic activity – a decrease in the concentration of methylene orange by 95-98 % is achieved when using the system TiO2: Cu NPs at a mass ratio of 10:1 and 5:1 components.

Damp and droop coefficient stability region analysis for interlinking converters with virtual asynchronous machine controllers in virtual energy storage systems

Although virtual energy storage systems (VESSs) based on virtual asynchronous machine (VAM) control strategy have been widely applied to microgrids to achieve power balance between supply and demand sides, damp and droop coefficients are variable due to the system operation state. It is prone to causing wideband oscillation, such as low-frequency and sub/super-synchronous oscillation. Thus, this paper proposes one damp and droop coefficient stability region identification approach based on the Guardian map theory for the interlinking converter (IC) of VESSs. Firstly, the VAM control method of IC is derived through the traditional asynchronous machine, and its small-signal model is further built. The aforesaid process is the important modeling basic. Secondly, the concept of the practical small signal stability region (P-SSSR) is proposed to make up for the deficiency of the traditional small signal stability region (SSSR) that cannot ensure system robustness. Thirdly, the mapping method based on translation and rotation mapping is introduced to ensure that the identification of the P-SSSR problem is switched into the Hurwitz matrix identification problem. Furthermore, the high-dimensional parameter stability region can be obtained through the Guardian map theory. Finally, the performance of the proposed method can be verified through simulation and experiment results.

Reduced dimensional Monte Carlo method: Preliminary integrations.

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least half of the integration variables prior to setting up the particular Monte Carlo calculation of interest, in some cases more. Proper accounting of invariant phase space structures shows that the system's dynamics is reducible into composite stable and unstable degrees of freedom. Stable degrees of freedom behave locally in the reduced dimensional phase space exactly as an analogous integrable system would. Classification of the unstable degrees of freedom is dependent upon the degree of chaos present in the dynamics. The techniques for deriving the requisite canonical coordinate transformations are developed and shown to block diagonalize the stability matrix into irreducible parts. In doing so, it is demonstrated how to reduce the amount of sampling directions necessary in a Monte Carlo simulation. The technique is illustrated by calculating return probabilities and expectation values for different dynamical regimes of a two-degrees-of-freedom coupled quartic oscillator within a classical Wigner method framework.

A probabilistic framework for describing a class of switching signals in continuous-time

We present an interpretation of switching signals with certain average dwell time in terms of Poisson process, which allows to build a probabilistic framework to accommodate all the switching signals of this kind. As a result, we can learn more knowledge about such signals. In particular, such a switching signal and the solution of the corresponding switching system jointly constitute a Markov process. And the Markov property will facilitate the asymptotic behaviour analysis of the switching dynamics. As a byproduct, we present an upper bound on the joint spectral radius of a family of Hurwitz or anti-Hurwitz matrices, which turns out to be quite sharp as compared with the existing results.

A new stabilized time-spectral finite element solver for fast simulation of blood flow

The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage the time-periodic nature of these flows by discretizing equations in the frequency domain instead of the time domain. This approach markedly reduces the size of the discrete problem and, consequently, the simulation cost. With this motivation, we introduce a finite element method for simulating time-periodic flows that are physically stable. The proposed time-spectral method is formulated by augmenting the baseline Galerkin’s method with a least-squares penalty term that is weighed by a positive-definite stabilization matrix. An error estimate is established for the convective–diffusive system, showing that the proposed method emulates the behavior of existing standard time methods including optimal convergence rate in diffusive regimes and stability in strong convection. This method is tested on a patient-specific Fontan model at nominal Reynolds and Womersley numbers of 500 and 10, respectively, demonstrating its ability to replicate conventional time simulation results using as few as 7 modes at 11% of the computational cost. Owing to its higher local-to-processor computation density, the proposed method also exhibits improved parallel scalability for fast simulation of time-critical applications.

Robust PID control of a tuned mass damper system and its stability analysis validation by Kharitonov and Edge theorems

ABSTRACT A robust control and stability analysis of a tuned mass damper attached to benchmark the model of mass-spring-damper system via different Kharitonov-related approaches, including the post-Kharitonov Edge Theorem, is presented in this paper. The control of uncertain parameters of the given system is demonstrated via robust Proportional-Integral-Derivative (PID) system tuning techniques in MATLAB. Usually, the Kharitonov theorem is sufficient to check the stability analysis of a controlled interval system. A detailed stability analysis of the given system by forming the Kharitonov rectangular parameter boxes and testing the positivity of Hurwitz determinants of the enclosed segments connecting opposite corners of the box is explained here. Stability checking is validated by the analysis based on the Hurwitz matrices of two Kharitonov polynomials. The multi-linear affine system model in the overall system plant is controlled and analysed via Edge theorem.

Non-fragile [formula omitted] filtering for delayed discrete-time Markov jump systems: An adaptive event-triggered strategy

This paper deals with the problem of non-fragile filter for delayed discrete-time Markov jump systems. The purpose is to design a mode-dependent filter such that the result filtering error system is stochastically stable and satisfies a prescribed H∞ performance lever γ. In order to improve the data transmission efficient, an adaptive event-triggered strategy is introduced. Then, with the help of the Lyapunov stability theory and matrix inequality, the sufficient conditions for the solution of the filter design problem proposed are established. Finally, two numerical examples are presented to verification the effectiveness of the proposed method.

Novel Proportional–Integral–Derivative Control Framework on Continuous-Time Positive Systems Using Linear Programming

This paper considers the proportional–integral–derivative (PID) control for continuous-time positive systems. A three-stage strategy is introduced to design the PID controller. In the first stage, the proportional and integral components of the PID control are designed. A matrix decomposition approach is used to describe the gain matrices of the proportional and integral components. The positivity and stability of the closed-loop systems without the derivative component of PID control are achieved by the properties of a Metzler and Hurwitz matrix. In the second stage, a non-negative inverse matrix is constructed to maintain the Metzler and Hurwitz properties of the closed-loop system matrix in the first stage. To deal with the inverse of the derivative component of PID control, a matrix decomposition approach is further utilized to design a non-negative inverse matrix. Then, the derivative component is obtained by virtue of the designed inverse matrix. All the presented conditions can be solved by virtue of a linear programming approach. Furthermore, the three-stage PID design is developed for a state observer-based PID controller. Finally, a simulation example is provided to verify the effectiveness and validity of the proposed design.

Leader-Following Consensus of Discrete-Time Nonlinear Multi-Agent Systems with Asymmetric Saturation Impulsive Control

Impulsive control is an effective approach for coordinating multi-agent systems in practical environments due to its high robustness and low cost. However, impulsive control exhibits characteristics such as high amplitude and rapid variation, potentially presenting threats to the equipment. Additionally, multi-agent systems are constrained by input saturation due to limitations in physical controller structures and information-processing capabilities. These saturation constraints may be asymmetrical. Therefore, it is necessary to consider the saturation constraint when implementing impulsive control, as it can also mitigate the threats posed by the impulse to agents. This paper investigates the leader-following consensus for a class of discrete-time nonlinear multi-agent systems, proposing an asymmetric saturation impulsive control protocol to reduce the energy consumption and damage to the equipment. Regarding the handle of asymmetric saturation, an approach is proposed that eliminates the need for transformation from the asymmetric case to the symmetric case, which retains the saturation function and directly introduces the sector condition to deal with saturation nonlinearity. Furthermore, based on Lyapunov stability theory and matrix theory, sufficient conditions for leader-following consensus in discrete-time nonlinear multi-agent systems under asymmetric saturation impulsive control are established, and the admissible region of the system is estimated. Finally, numerical simulations are provided to verify the validity of the theoretical results.

Prediction of Onset Temperature in Standing Wave Thermoacoustic Engine with Mesh Screen Stack

A thermoacoustic engine is a engine that converts thermal energy into acoustic energy, which can be used to generate electricity or cooling. This engine is attractive because it consists only of a stack, heat exchangers, and a resonator. The stack serves as the primary component for the energy conversion process and consists of porous materials like an array of stainless steel mesh screens. To generate the acoustic energy, a minimum temperature difference is necessary between the two sides of the stack, called the onset temperature difference. However, the calculation for prediction of onset temperature on the stack made of mesh screen has not been addressed. Therefore, the objective of this paper is to propose a method that can be used to estimate the onset temperature difference in standing wave thermoacoustic engine with stacks made of mesh screen arrays. The onset temperature difference is predicted numerically using linear stability theory and matrix transfer methods. Experimental verification is carried out by using standing wave thermoacoustic engine from pervious study. The results showed that the lowest onset temperature difference (TH - TC = 140ºC) is obtained when rh = 0.497 mm. Furthermore, the numerical and experimental onset temperature difference comparisons show a qualitative agreement, allowing the onset temperature prediction method to be used in designing standing wave thermoacoustic engines with stacks made of mesh screens.

Laser-optimized Pt-Y alloy nanoparticles embedded in Pt-Y oxide matrix for high stability and ORR electrocatalytic activity

The development of active yet stable catalysts for oxygen reduction reaction (ORR) is still a major issue for the extensive permeation of fuel cells into everyday technology. While nanostructured Pt catalysts are to date the best available systems in terms of activity, the same is not true for stability, particularly under operating conditions. In this work, PtXY alloy nanoparticles are proposed as active and durable electrocatalysts for ORR. PtXY nanoalloys are synthesized and further optimized by laser ablation in liquid followed by laser fragmentation in liquid. The novel integrated laser-assisted methodology succeeded in producing PtxY nanoparticles with the ideal size (<10 nm) of commercial Pt catalysts, yet resulting remarkably more active with E1/2 = 0.943 V vs. RHE, specific activity = 1095 μA cm−2 and mass activity > 1000 Ag−1. At the same time, the nanoalloys are embedded in a fine Pt oxide matrix, which allows a greater stability of the catalyst than the commercial Pt reference, as directly verified on a gas diffusion electrode.

In-Situ Convertible Amorphous Silicon Nitride (SiNx) Anode: Resolving the Long-Term Cyclic Instability of Silicon

Silicon (Si) has shown its promises as anode material for next-generation high-energy lithium-ion batteries (LIBs) due to its high theoretical capacity1. However, its practical application has been impeded by the severe cyclic instability caused by a large volume change during (de) lithiation. Recently, a new family of silicon-based anode materials called “in-situ convertible-type anode materials” has emerged to resolve the cyclic instability of silicon.2,3 This family includes sub-stoichiometric oxides, nitrides, and carbides of silicon (SiAx, where A = N, C, O). The working principle of these materials follow two mechanisms: (1) irreversible conversion and (2) reversible alloying/dealloying. During initial lithiation, the conversion reaction occurs, forming Si-Li nanodomains inside a stable Li-conductive matrix denoted as LiySixA (A=N, C, O). In the subsequent cycles, the Si-Li nanodomains reversibly alloying/dealloying with Li, while the Li-conductive matrix ensures stable cycling and good rate capability. Such composition mitigates the challenges associated with Si’s large volume change ensuring long-term cyclic stability.In this study, we demonstrate our approach on the development of silicon-rich, sub-stochiometric, amorphous silicon nitride (SiNx) nanoparticles, as an in-situ convertible-type anode material and its long-term cyclic performance for LIBs. In this approach, the SiNx nanoparticles are produced via the decomposition of silane gas in the presence of ammonia using an industrially scalable, free space reactor (FSR), which is developed and customized in our research institute (IFE) (Fig. 1a). Proper proportions of silane and ammonia gases are introduced into the reactor, leading to the nucleation and growth of SiNx nanoparticles. The synthesized SiNx nanoparticles exhibited Si-rich domain and amorphous structure with particle size between 100 nm - 200 nm (Fig. 1b), as confirmed by SEM, TEM and XRD characterizations. The presence of nitrogen in silicon dominated composition is revealed by energy dispersive electron spectroscopy (EDS) and Fourier-transform infrared spectroscopy (FTIR). The scalability and reproducibility of the FSR synthesis method makes it a promising approach for the industrial production of SiNx for advance anode materials for LIBs.The electrochemical performance of the synthesized SiNx anode is evaluated by galvanostatic cycling and electrochemical impedance spectroscopy. The electrochemical performance of the SiNx performed on the electrodes with the active mass loading of 0.987 mg/cm2 and cycled at C/5 rate has preserved its capacity about 852 mAh/g after around 600 cycles. As seen from Fig. 1c, the improved cyclic stability of the SiNx compared with pure silicon indicates that the Li-conductive matrix plays crucial role in stabilizing the anode. The authors emphasize the need for further investigation and collaboration, particularly in advance characterization, to better understand the composition and mechanisms of the Li-conductive matrix in the SiNx anode. Such detailed understanding can significantly benefit the conversion-type anode materials for their widespread use in future LIB technologies.References Zuo, X., Zhu, J., Müller-Buschbaum, P. & Cheng, Y.-J. Silicon based lithium-ion battery anodes: A chronicle perspective review. Nano Energy 31, 113–143 (2017).Ulvestad, A. et al. Stoichiometry-Controlled Reversible Lithiation Capacity in Nanostructured Silicon Nitrides Enabled by in Situ Conversion Reaction. ACS Nano 15, 16777–16787 (2021).Kilian, S. O. et al. Active Buffer Matrix in Nanoparticle-Based Silicon-Rich Silicon Nitride Anodes Enables High Stability and Fast Charging of Lithium-Ion Batteries. Advanced Materials Interfaces 9, 2201389 (2022). Figure 1

Simultaneous Immobilization of Heavy Metals in MKPC-Based Mortar-Experimental Assessment.

Heavy metal contamination, associated with the increase in industrial production and the development of the population in general, poses a significant risk in terms of the contamination of soil, water, and, consequently, industrial plants and human health. The presence of ecotoxic heavy metals (HMs) thus significantly limits the sustainable development of society and contributes to the deterioration of the quality of the environment as a whole. For this reason, the stabilization and immobilization of heavy metals is a very topical issue. This paper deals with the possibility of the simultaneous immobilization of heavy metals (Ba2+, Pb2+, and Zn2+) in mortar based on magnesium potassium phosphate cement (MKPC). The structural, mechanical, and hygric parameters of mortars artificially contaminated with heavy metals in the form of salt solutions were investigated together with the formed hydration products. In the leachates of the prepared samples, the content of HMs was measured and the immobilization ratio of each HM was determined. The immobilization rate of all the investigated HMs was >98.7%, which gave information about the effectiveness of the MKPC-based matrix for HM stabilization. Furthermore, the content of HMs in the leachates was below the prescribed limits for non-hazardous waste that can be safely treated without any environmental risks. Although the presence of heavy metals led to a reduction in the strength of the prepared mortar (46.5% and 57.3% in compressive and flexural strength, respectively), its mechanical resistance remained high enough for many construction applications. Moreover, the low values of the parameters characterizing the water transport (water absorption coefficient Aw = 4.26 × 10-3 kg·m-2·s-1/2 and sorptivity S = 4.0 × 10-6 m·s-1/2) clearly demonstrate the limited possibility of the leaching of heavy metals from the MKPC matrix structure.

Impedance-Based Stability Analysis of Grid-Connected Inverters under the Unbalanced Grid Condition

As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments.

Development of a novel UHPLC-MS/MS method for the quantification of corynoxeine: Application to pharmacokinetics and tissue distribution studies in normal and chronic unpredictable mild stress-induced depression rats

Corynoxeine, a natural active alkaloid found in Genus Uncaria, has been reported to have anti-depressant effects. In this study, a sensitive and efficient ultra-high performance liquid chromatography tandem mass spectrometry method for quantifying corynoxeine in rat plasma and tissues was established, validated and applied to investigate the pharmacokinetics and tissue distribution differences between normal rats and chronic unpredictable mild stress (CUMS)-induced depression model rats following oral administration. All bio-samples were prepared by methanol protein precipitation method with theophylline as internal standard (IS). Chromatographic separation was conducted on an Agilent ZORBAX Eclipse Plus C18 column using mobile phase A (acetonitrile) and B (0.1% formic acid in water) in gradient elution mode with a flow rate of 0.3 mL/min. Mass spectrometric detection was performed in multiple-reaction monitoring mode with positive electrospray ionization source. The transitions of m/z 383.0→160.2 for corynoxeine and m/z 181.1→124.0 for IS were chosen for quantification. The method showed good linearity, stability, accuracy, precision, recovery, and non-significant matrix effect, which were within the acceptable ranges. The pharmacokinetic results revealed that the absorption and bioavailability of corynoxeine in depression rats decreased compared to normal rats. The tissue distribution of corynoxeine trended to be mostly in the intestine and stomach and the distribution of this compound in intestine tissue of depression rats was significantly increased compared to the normal rats. The pharmacokinetics and tissue distribution profiles of corynoxeine were altered in CUMS-induced depression rats compared to normal rats and these experimental findings could provide beneficial information to the mechanism research and clinical applications of corynoxeine.

Event-Triggered Sliding-Mode Control for Fuzzy Semi-Markovian Jump Systems With Dead Zone Input and Application to Circuit Systems

This paper investigates event-triggered sliding mode control (SMC) for fuzzy semi-Markovian jump systems (S-MJSs) subject to limited communication capacity, in which we consider the network-induced transmission delay, dead-zone input and partially unknown transition rates of jumping mode in a whole framework. First, an event-triggered mechanism(ETM) is employed in the sensor-to-controller channel to save network resources efficiently. Then, a novel integral sliding surface is obtained with the aid of the event-triggered state information, and some new sufficient conditions on the stochastic stability of the overall closed-loop system are given in the sense of partially unknown transition rates via stochastic stability theory and matrix inequality method. Furthermore, a mode-depended sliding mode controller is designed to guarantee the reachability of the sliding surface in finite time by using the Lyapunov stability theory. Finally, a TD circuit model is provided to illustrate the validity of the proposed control scheme.

Outer Synchronization of Two Muti-Layer Dynamical Complex Networks with Intermittent Pinning Control

This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response configuration, and sufficient conditions to achieve the outer synchronization are derived based on the Lyapunov stability theory and matrix inequalities. Second, outer synchronization problem of multi-layer networks is discussed by setting an adaptive intermittent pinning controller; an appropriate Lyapunov function is selected to prove the criteria of synchronization between the drive multi-layer network and the response multi-layer network. Finally, three simulation examples are given to show the effectiveness of our control schemes.