Stability Criterion Research Articles

The Frequency-Domain Criterion for Quadratic Stability of Discrete Systems with Switching between Three Linear Subsystems

The Frequency-Domain Criterion for Quadratic Stability of Discrete Systems with Switching between Three Linear Subsystems

Input-to-state stability of switched systems with counter-dependent multiple discontinuous Lyapunov function

This paper investigates the input-to-state stability (ISS) of switched systems under the mode-dependent average dwell time (MDADT) switching. A new non-equidistant partitioning (NEP) method for maximum and actual dwell time intervals is proposed, enhancing the flexibility in constructing the Lyapunov function. Building upon the proposed NEP method, a novel counter-dependent multiple discontinuous Lyapunov function (CDMDLF) is constructed by incorporating a counter, where the value of the counter is the partitioning number of the current mode-running time interval. Furthermore, the evolution of Lyapunov functions at adjacent partitioning points dynamically depends on the previous partitioning point rather than a fixed constant, which is more flexible and practical. Utilizing the developed CDMDLF, some less conservative stability criteria are established for nonlinear and linear switched systems. It is revealed that our proposed method covers the multiple discontinuous Lyapunov function (MDLF) and the switching-signal-based MDLF (SMDLF) methods as exceptional cases while providing tighter bounds on the MDADT. In the end, two numerical examples are given to illustrate the advantages and effectiveness of the presented approach.

Exploring the physical characteristics of chalcogenide SrZrS3 perovskite: Insights for photovoltaic use

AbstractIn this study, first-principle-based Density functional Theory (DFT) have been utilized to investigate the electronic, optical, mechanical and thermal properties of SrZrS3 for the solar cell application. Semiconducting nature of SrZrS3 was found via the investigation of electronic band structure and density of state (DOS). Electronic band structures reveal direct bandgap semiconductor properties with values 0.57 eV in Perdew-Burke-Ernzerhof functional (PBE) method, and 1.28 eV is in hybrid Functional (HSE06) method for SrZrS3, suggesting specific applications in photovoltaic (PV) cell. Significant constant such as absorption, reflectivity, refractivity, and loss function were also calculated to evaluate the optical properties of SrZrS3. The optical properties highlight the potential of SrZrS3 material for optoelectronic and photovoltaic applications. The Born stability criteria confirmed the mechanical stability of this compound. Furthermore, its minimum thermal conductivity (Kmin = 0.66 Wm−1 K−1) is adequate for maintaining performance without excessive heat buildup, making it suitable for high-efficiency solar cells. Graphical Abstract

Theoretical and numerical bifurcation analysis in a prey–predator model with prey harvesting effort

This paper explores the influence of harvest efforts on a discrete-time prey–predator model. We established the stability criteria for fixed points in the proposed model. We investigate codim-1 and codim-2 bifurcations, exploring a range of multiple and generic bifurcations within the discrete model. The model demonstrates fold, flip, and Neimark–Sacker bifurcations, as well as resonances such as 1:2, 1:3, and 1:4 at distinct fixed points. Through the application of the critical normal form theorem and bifurcation theory, we calculate normal form coefficients for each bifurcation. Our results show that an excessive prey harvest rate can actually destabilize the model dynamics. Numerical simulations validate our findings, shedding light on the intricate dynamics of the system.

Ecosystem stability relies on diversity difference between trophic levels

The stability of ecological communities has a profound impact on humans, ranging from individual health influenced by the microbiome to ecosystem services provided by fisheries. A long-standing goal of ecology is the elucidation of the interplay between biodiversity and ecosystem stability, with some ecologists warning of instability due to loss of species diversity while others arguing that greater diversity will instead lead to instability. Here, by considering a minimal two-level ecosystem with multiple predator and prey species, we show that stability does not depend on absolute diversity but rather on diversity differences between levels. We found that increasing diversity in either level first destabilizes but then stabilizes the community (i.e., a reentrant stability transition). We therefore find that it is the diversity difference between levels that is the key to stability, with the least stable communities having similar diversities in different levels. An analytical stability criterion is derived, demonstrating quantitatively that the critical diversity difference is determined by the correlation between how one level affects another and how it is affected in turn. Our stability criterion also applies to consumer-resource models with other forms of interaction such as cross-feeding. Finally, we show that stability depends on diversity differences in ecosystems with three trophic levels. Our finding of a nonmonotonic dependence of stability on diversity provides a natural explanation for the variety of diversity-stability relationships reported in the literature, and emphasizes the significance of level structure in predicting complex community behaviors.

Non-monotonically changes in double Schottky barrier of MnCO3–doped ZnO varistors during DC aging

Abstract ZnO varistors play a crucial role as core component in metal oxide arresters due to their excellent nonlinear current density-electrical field (J–E) characteristics. After long-term operation under DC stress (DC aging), the J–E curves of ZnO varistors invented in the last decade cross with the original curve. Unexpectedly, the ‘crossover’ phenomenon cannot be explained by the vastly-accepted ion migration mechanism by which the barrier height monotonically declines after DC aging. In the present study, aging and recovery experiments were carried out on MnCO3-doped ZnO varistors. The symmetry of J–E characteristics in the same direction as and the opposite direction to the DC stress was compared, parameters of double Schottky barrier were analyzed, and evolution of point defects was deduced using dielectric spectra. It was found that, in addition to ion migrations, there are electrons ionized by zinc interstitials filling the interface states in the early stage of aging. Because these processes are dominant in different stages, the barrier height changes non-monotonically. MnCO3 can suppress the formation of zinc interstitials, so it simultaneously inhibits ion migrations and filling of the interface states by electrons. When 0.38 mol% MnCO3 is doped, J–E characteristics and the Schottky barrier of ZnO varistors show the smallest deviations during aging and recovery. The findings are helpful in updating criteria for the long-term stability of ZnO varistors and suggest that modifications to their formulae targeting the suppression of the filling the interface states by electrons are also expected to bolster the stability.

Anisotropic quark stars in $f(R,L_m,T)$ gravity

Abstract We investigate the impact of $f(R,L_m,T)$ gravity on the internal structure of compact stars, expecting this theory to manifest prominently in the high-density cores of such stars. In this study, we begin by considering the algebraic function $f(R,L_m,T) = R + \alpha T L_m$, where $\alpha$ represents the matter-geometry coupling constant. We specifically choose the matter Lagrangian density $L_m= -\rho$ to explore compact stars with anisotropic pressure. To this end, we employ the MIT bag model as an equation of state. We then numerically solve the hydrostatic equilibrium equations to obtain mass-radius relations for quark stars, examining static stability criteria, the adiabatic index, and the speed of sound. Finally, we use recent astrophysical data to constrain the coupling parameter $\alpha$, which may lead to either larger or smaller masses for quark stars compared to their counterparts in general relativity.

Asymmetric LKF approach for stability analysis of multi-area load frequency control systems with time-varying delays

ABSTRACT The widespread use of communication networks in power systems to send and receive control signals causes time delays in the feedback loop. Improper handling of these delays might degrade controller performance or cause system instability. This work presents new stability criteria that are less conservative in analysing the influence of delays on the stable operation of PI controller-based multi-area power systems with uncertainties and disturbances. An asymmetric Lyapunov-Krasovskii functional technique is used to reduce conservatism by relaxing the condition that all matrices associated with the LKF formulation need not be symmetric or have positive definiteness. In contrast, the symmetric LKF requires all matrices to be symmetric. Two tight-bound integral inequalities are implemented to compute the quadratic integral terms included in the derivative of asymmetric LKF. The less conservative stability conditions are derived for multi-area LFC systems subjected to delays, parameter uncertainties, and disturbances by utilising asymmetric LKF. The superiority of the proposed stability criterion is determined both theoretically and through simulation. According to the analysis, the proposed stability criterion provides higher delay margins than existing techniques.

Dynamic interplay of anisotropy and matter-geometry coupling in stellar structures: A comprehensive study on the stability of pulsars 4U 1820-30 and LMC X-4

This study investigates the behavior of dense celestial objects within the context of f(R,Lm,T) theory. We develop modified Einstein field equations that account for the anisotropic configured static interior spacetime. By applying two specific constraints associated with the radial metric function and anisotropic pressure, we find a couple of solutions to these highly non-linear gravitational equations. For both models, we encounter differential equations whose integration yield constants which are determined through matching conditions. Additionally, the requirement of vanishing radial pressure at the hypersurface also plays an important role in this context. Furthermore, we graphically evaluate certain conditions whose fulfillment ensures the model’s feasibility under different parametric values. For this, we take into account the observational data of two compact stars 4U 1820-30 and LMC X-4. We conclude both our models to be well-aligned with the required viability and stability criteria. We must highlight here that our study advances the understanding of how f(R,Lm,T) gravity affects the internal structure of compact stars, providing valuable insights for future explorations.

Concept of synthesis of the digital twin of the rock massif based on the stability criterion

Concept of synthesis of the digital twin of the rock massif based on the stability criterion

The [formula omitted]th moment stability of stochastic functional differential equations with mixed time-varying delay and its applications

This paper investigates the pth moment stability with general decay rate for stochastic mixed time-varying delay functional differential equations with semi-Markov switching and Lévy noise (SMDFDEs-SMS-LN). By employing multiple degenerate Lyapunov functionals, the non-negative martingale convergence theorem, and functional Itô’s formula, a criterion for assessing the pth moment stability with general decay rate is derived. Auxiliary functions with multiple time-varying coefficients are introduced to regulate the diffusion operator, which enhances the system’s adaptability to high-order nonlinear coefficients. These conditions are applied to a stochastic mixed-delay neural network with semi-Markov switching and Lévy noise (SMDNN-SMS-LN) and a scalar non-autonomous stochastic mixed time-varying delay functional differential equations with semi-Markov switching and Lévy noise system with non-global Lipschitz conditions. Using vertex method and linear matrix inequalities, the pth moment stability criteria with general decay rate for the above systems are respectively derived. Finally, the effectiveness of the obtained results is validated through two numerical examples.

Stabilization of chaotic quaternion-valued neutral-type neural networks via sampled-data control with two-sided looped functional approach

The quaternion-valued neutral-type neural networks (QVNTNNs) stability problem through designing sampled-data controller is investigated in this paper. A main stability criterion of the considered neural networks (NNs) is obtained in the form of linear matrix inequalities (LMIs) based on the two-sided looped functional method. The effectiveness of the criterion is shown by a numerical example. It needs to be emphasized that the considered QVNTNNs model in this paper is not broken down into real-valued or complex-valued models in stability analysis, and the acquired criterion holds for both real-valued and complex-valued NNs.

Spherically symmetric perfect fluid filled universe within the 4 dimensional Einstein–Gauss–Bonnet gravity formalism with vanishing conformal curvature

Conformally flat spacetime geometry is of immense physical importance. In this conext we obtain the most general solutions for 4 dimensional Einstein-Gauss–Bonnet (4D EGB) static spherically symmetric spacetimes. The standard Schwarzschild incompressible fluid sphere is one possible solution, however, new branches of solutions emerge that have cosmological significance. It is intriguing that the geometry of the new model is given by an exactly known spatially directed potential while the remaining potential is given as an integral. It is not necessary to know the explicit form of the temporally directed potential to analyse the physics of the model. However, at least two explicit exact solutions for both potentials are exhibited. Graphical plots are constructed to show that barring a short interval from the centre of the distribution which may be excised and replaced with a well-behaved fluid, all the elementary physical tests are successful. The model considered does not admit a finite radius hence is not applicable to astrophysical compact objects however the pleasing physical characteristics of the fluid suggests applicability to a perfect fluid filled universe. The model satisfies the causality requirement preventing the sound speed from becoming superluminal as well as the Chandrasekar stability criterion demanded of adiabatic fluids. Moreover all the energy conditions are complied with. The analysis effectively rules out the existence of conformally flat stars in 4D EGB gravity aside from the interior Schwarzschild spacetime.

Heat and Mass Transfer in Unsteady MHD Casson Fluid Flow Over a Semi-Infinite Vertical Plate Through Porous Medium with Dissipative and Radiative Effects

Nowadays, Casson fluid and its diverse applications are highly effective across a vast array of industrial, biological and environmental sectors, due to its unique flow properties. This study focuses on the numerical investigation of the heat and mass transfer characteristics of an unsteady incompressible Casson fluid flow over a semi-infinite vertical flat plate by considering free convection effects. The fluid is conducting the electrical current as it moves through the porous medium. The formulation of the governing equation is based on the use of this phenomenon. In the model, the formulated governing equations are converted into non-dimensional form first, and the MHD mathematical model is analyzed using the boundary conditions. The scheme of finite difference method is implemented to solve the model, where concentration profiles are also discussed. Stability and convergence criteria are applied for the accuracy of numerical techniques, and the effects of various parameters on skin friction, rate of heat and mass transfer have been examined significantly. The results indicate that the temperature of the plate increases with the increase in the value of the magnetic parameter for the Casson fluid but the reverse is observed in its limiting case. The present results are compared and checked with previously published results and a remarkable conclusion is given at the end of the study.

Numerical simulation of intact stability analysis of a catamaran vessel

This research work shows the intact stability analysis of a passenger catamaran vessel considering their different load cases: Fully loaded ship to maximum free-board draught; lightship with full tanks; and lightship with no passengers, crew, and empty tanks. The MAXSURF package as the Naval Architecture tool was selected to model the catamaran hull form design using the MAXSURF modeler and the MAXSURF stability was employed to carry out the stability analysis. The stability analysis was conducted using the intact stability criteria of IMO. The stability assessment was performed to verify whether the vessel's stability complies with international standards. A numerical method (Simpson’s rules) was employed in evaluating the area under the GZ curves within the range: 0º - 30º; 0º - 40º; 30º - 40º. The maximum heeling moment was calculated as 954.48 tons-m for load case 1; 755.36 tons-m for load case 2; 671.58 tons-m for load case 3 and the range of stability for all three load cases was justified well. It was concluded that the Catamaran at full load (Load case 1) is more stable with a maximum heeling moment of 954.48 tons-m as compared to Load cases 2 and 3

Predefined time convergence guaranteed performance control for uncertain systems based on reinforcement learning

The prescribed performance control method (PPCM) is commonly employed to ensure the guaranteed performance control of non-linear systems. However, traditional approaches suffer from certain drawbacks, such as the dependence of parameter settings for the performance constraint function on the initial tracking error value and the inability to specify the convergence time of tracking error according to engineering requirements. This paper focuses on designing a fault tolerant control strategy with prescribed convergence time and prescribed transient performance for uncertain systems, considering parameter perturbance, actuator faults, and unknown initial states. Firstly, we introduce an error conversion function that transforms the tracking error with any initial value into a new error variable starting from zero. This resolves the issue of depending on the initial value of tracking error in setting parameters for the performance constraint function in prescribed performance control methods. Subsequently, we derive a novel Lyapunov stability criterion for predefined time (PDT) convergence and design a fault-tolerant control strategy using backstepping control method while ensuring prescribed convergence time and prescribed performance. In this approach, we propose a new online reinforcement learning intelligent algorithm to estimate compound interference caused by actuator faults, control saturation constraint increment, system parameter perturbation, and external interference. The theoretical proof establishes predefined time convergence of the closed-loop system. Finally, numerical simulations are conducted on industrial robots with actuator faults to validate the effectiveness of our designed control strategy.

Examining the behavior of a two-connected-spring pendulum according to non-resonance and resonance conditions

This paper focuses on the planar forced oscillations of a particle linked to its support point through a system comprising two nonlinear springs arranged in series with two viscous dampers. The motion of this point is restricted to being on an elliptic route. Three degrees-of-freedom (DOF) characterize the system’s motion, explained by two differential equations (DEs) and another algebraic equation derived using Lagrange’s equations. The traditional method of multiple-time scales (MMTS) is applied in the context of the time realm. The dynamics of forced and damped oscillations is explored in this work, highlighting non-resonant conditions along with two distinct external resonances. Furthermore, stationary periodic states influenced by external resonances are examined, and the stability of each case is evaluated. The asymptotic solutions of the controlling equations are solved up to the third approximation. The classification of resonance cases is based on the second and third order of the approximate solutions. Therefore, the solvability criteria and the modulation equations (ME) are obtained. The Routh–Hurwitz conditions (RHCs) serve as the basis for assessing the stability and instability criteria. A discussion and graphical representations of the time histories, frequency response curves (FRC), and stability regions are provided to demonstrate the beneficial effects of different physical parameter inputs on the system’s performance. The obtained outcomes can improve the performance of spring-based mechanical systems like vibrational isolation devices, shock absorbers, and suspension mechanisms. Additionally, they have the potential to enhance stability and control in robotic limbs and aircraft landing gear systems, ensuring better stress absorption and stability.

Construction and Initial Validation of Measures Regarding Human Milk Donation: An Application of the Theory of Planned Behavior

Objective: to construct and validate measures related to human milk donation (HMD), based on the theory of planned behavior (TPB). Theoretical framework: it is assumed that TPB can be used to explain and predict HMD behavior and the construction of these measures should consider reflective and formative measures. Method: a questionnaire was developed with 12 direct reflective measures and 30 indirect formative measures and applied to a sample of postpartum women eligible to donate. The reliability of the direct measures was verified by the internal consistency criterion, using Cronbach's alpha and composite reliability. The reliability of the indirect measures was verified by the temporal stability criterion, using the test-retest technique and the intraclass correlation coefficient. The construct validity of the direct measures was established through the convergent and discriminant validity of these measures. The construct validity of the indirect formative measures was established through convergent validity, the assessment of collinearity problems and the assessment of the significance and relevance of the formative measures. Results and conclusion: the reliability and validity of the direct reflective and indirect formative measures indicated that they are reliable and acceptable. Research implications: this questionnaire can be used to predict HMD behavior, which in turn can improve donor recruitment management in human milk banks. Originality/value: a questionnaire with direct and indirect measures of the TPB on HMD is unprecedented.

Stability of Standing Periodic Waves in the Massive Thirring Model

ABSTRACTWe analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability of the standing periodic waves can be studied by using their Lax spectrum. We show analytically that each family of standing periodic waves is distinguished by the location of eight eigenvalues which coincide with the end points of the spectral bands of the Lax spectrum. The standing periodic waves are proven to be spectrally stable if the eight eigenvalues are located either on the imaginary axis or along the diagonals of the complex plane. By computing the Lax spectrum numerically, we show that this stability criterion is satisfied for some standing periodic waves.

Application of Mathematics for Robust Stability and for Robustly Strictly Positive Real on an Uncertain Interval Plant

ABSTRACTIn this article, we present a robust control problem wherein represents a family of interval plants. For this particular problem, we introduce four Kharitonov polynomials uniquely by minimizing and maximizing the concept of multilinear functions with uncertain parameters and for the plant and where denotes the conjugate of and , with representing frequency within a specified domain. This technique yields a Kharitonov rectangle or box whose every four vertices are represented by four unique Kharitonov polynomials , each is denoted by and and this rectangle characterizes both robust stability and robustly strictly positive real (SPR) for the family of interval plants (). Thus, the introduction of this Kharitonov rectangle stands as a novel innovation in this article. Our contribution encompasses two key aspects. Initially, we demonstrate the stability of the four unique Kharitonov polynomials employing Hurwitz stability criteria, followed by the utilization of Kharitonov's theorem to ensure robust stability of . Subsequently, to establish robustly SPR of , we analyze the SPR of each interval plant concerning the stability of and , adhering to the condition . Additionally, we provide a detailed illustrative example. Furthermore, we demonstrate the motion of the Kharitonov rectangle and the robust stability test through simulation.