Stability Of Such Systems Research Articles

Resilience Analysis for Double Spending via Sequential Decision Optimization

Recently, diverse concepts originating from blockchain ideas have gained increasing popularity. One of the innovations in this technology is the use of the proof-of-work (PoW) concept for reaching a consensus within a distributed network of autonomous computer nodes. This goal has been achieved by design of PoW-based protocols with a built-in equilibrium property: If all participants operate honestly then the best strategy of any agent is also to follow the same protocol. However, there are concerns about the stability of such systems. In this context, the analysis of attack vectors, which represent potentially successful deviations from the honest behavior, turns out to be the most crucial question. Naturally, stability of a blockchain system can be assessed only by determining its most vulnerable components. For this reason, knowing the most successful attacks, regardless of their sophistication level, is inevitable for a reliable stability analysis. In this work, we focus entirely on blockchain systems which are based on the proof-of-work consensus protocols, referred to as PoW-based systems, and consider planning and launching an attack on such system as an optimal sequential decision-making problem under uncertainty. With our results, we suggest a quantitative approach to decide whether a given PoW-based system is vulnerable with respect to this type of attack, which can help assessing and improving its stability.

The stability of differential-difference equations with proportional time delay. I. Linear controlled system

The article considers a controlled system of linear differential-difference equations with a linearly increasing delay. Sufficient conditions for the asymptotic stability of such systems are known; however, general conditions for the stabilizability of controlled systems and constructive algorithms for constructing stabilizing controls have not yet been obtained. For a linear differential-difference equation of delayed type with linearly increasing delay, the canonical Zubov transformation is applied and conditions for the stabilization of such systems by static control are derived. An algorithm for checking the conditions for the existence of a stabilizing control and for its constructing is formulated. New theorems on stability analysis of systems of linear differential-difference equations with linearly increasing delay are proven. The results obtained can be applied to the case of systems with several proportional delays.

An extension of a Lyapunov approach to the stabilization of second order coupled systems

This paper deals with the convergence to zero of the energy of the solutions of a second order linear coupled system. It revisits some previous results on the stabilization of such systems by exhibiting Lyapunov functions. The ones used are constructed according to some scalar cases situations. These simpler situations explicitely show that the assumptions made on the operators in the coupled systems seem, first, natural and, second, give insight on their forms.

Hydrogen Bonding Interaction and Structural Change in Some Aliphatic Alcohol-Water Complexes: A Quantum Mechanical MP4 Study

Hydrogen bonding interaction in low molecular weight alcohols or lower alcohol (viz. methanol and ethanol) with water molecule is quite common. But, due to the presence of bulky groups in higher alcohols (viz. propanol, butanol and pentanol and their isomers) the hydrogen bonding interaction between alcohol and water molecule is significantly different. In alcohol-water heterodimer complexes, water plays an important role in the stability of such system, alcohol will be interacting with water molecule either as proton donor or proton acceptor mode. Quantum mechanical method, fourth degree Møller-Plesset (MP4) perturbation theory is an important tool for computing the interaction energy between the alcohol-water complexes. The interaction energy (IE) and natural bond orbital (NBO) calculations for some common aliphatic alcohol-water complexes (e.g. methanol, ethanol, propanol, butanol and pentanol) and their isomers were computed by using MP4 method.

Semiconductor-based photocatalysts for photocatalytic and photoelectrochemical water splitting: will we stop with photocorrosion?

This review outlines recent advances in strategies to improve the photoreaction stability of photocatalytic/photoelectrochemical water splitting systems, and discusses the tactics involved in improving the stability of such systems with different photocorrosion mechanisms.

Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays

This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.

Stability analysis by averaging: a time-delay approach

We study stability of linear systems with fast time-varying coefficients. The classical averaging method guarantees the stability of such systems for small enough values of parameter provided the corresponding averaged system is stable. However, it is difficult to find an upper bound on the small parameter by using classical tools for asymptotic analysis. In this paper we introduce an efficient constructive method for finding an upper bound on the value of the small parameter that guarantees a desired exponential decay rate. We transform the system to a model with time-delays of the length of the small parameter. The resulting time-delay system is a perturbation of the averaged LTI system which is assumed to be exponentially stable. The stability of the time-delay system guarantees the stability of the original one. We construct an appropriate Lyapunov functional for finding sufficient stability conditions in the form of linear matrix inequalities (LMIs). The upper bound on the small parameter that preserves the exponential stability is found from LMIs. Two numerical examples (stabilization by vibrational control and by time-dependent switching) illustrate the efficiency of the method.

Exploitation of Natural Resources in Oil and Gas Industry: Common Factors of Use and Conservation of Ecological Systems

The lack of a realistic estimate of the natural capital largely determines the economic and ecological problems in different sectors of economy. Economically inefficient use of the natural capital leads to its depletion. Flouting of environmental laws, when developing and applying technologies of exploitation of natural resources, has a detrimental effect on the environment, destroying the ecological systems. Exploitation of natural resources in oil and gas industry and development of highly sophisticated natural-engineering systems cause disruption of the ecological balance in the environment and shift in the balance of the environmental components: matter, energy and information. Stabilization of such systems and restoring their disturbed or lost balance puts the attitude towards the environment as a natural system in the forefront. Resistance of this system is regulated by natural environmental laws. Unbiased evaluation of the state of the natural-engineering system in exploitation of natural resources should be given on the basis of the system analysis. Such analysis presupposes interaction and interdependence of all the components and also internal and external interrelations of natural and technogenic subsystems. The analysis requires an integrated approach to consider the processes of use of raw materials, pollution of the biosphere components with hydrocarbons and other substances, and also risk assessment of their negative impact through biogeochemical cycles. Due to the increase of the share of difficult oil, deterioration of its quality, creation of new centres of exploitation of natural resources, it has become essential to find ecologically and economically substantiated solutions taking into account natural laws.

Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses

The finite-time Mittag-Leffler stability for fractional-order quaternion-valued memristive neural networks (FQMNNs) with impulsive effect is studied here. A new mathematical expression of the quaternion-value memductance (memristance) is proposed according to the feature of the quaternion-valued memristive and a new class of FQMNNs is designed. In quaternion field, by using the framework of Filippov solutions as well as differential inclusion theoretical analysis, suitable Lyapunov-functional and some fractional inequality techniques, the existence of unique equilibrium point and Mittag-Leffler stability in finite time analysis for considered impulsive FQMNNs have been established with the order $$0<\beta <1$$. Then, for the fractional order $$\beta $$ satisfying $$1<\beta <2$$ and by ignoring the impulsive effects, a new sufficient criterion are given to ensure the finite time stability of considered new FQMNNs system by the employment of Laplace transform, Mittag-Leffler function and generalized Gronwall inequality. Furthermore, the asymptotic stability of such system with order $$1<\beta <2$$ have been investigated. Ultimately, the accuracy and validity of obtained finite time stability criteria are supported by two numerical examples.

Stability Analysis of Linear Polytopic Descriptor Systems Using a Novel Copositive Matrix Approach

In this paper, we propose a copositive matrix approach to study stability of linear descriptor systems with polytopic uncertainty. First, by using copositive matrix analysis, new stability conditions are established in terms of linear matrix inequalities ensuring the regularity, impulse free, and exponential stability of such systems. Then, we use the obtained results to provide stability conditions for the system with delay. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Eigenvalue-Oriented Dynamic Stability Examination to Enhance Designing a Microgrid Hosting Clusters of Inertial and Non-Inertial Distributed Generators

Self-governing microgrids may consist of several conventional synchronous generators, converter-based distributed resources, and energy storages. In this paper, an eigenvalue-oriented stability assessment method is established to study the small signal stability of such systems that have complex dynamic characteristics. A new index referred to as the microgrid's marginal frequency stability index is established. This index is then used to determine the influence and correlation between sizes, quantities and internal parameters of the resources and loads on the microgrid's stability. Likewise, using this index, the impact of the isolation and coupling impedance amongst resources and loads are studied on the microgrid's stability. The findings of this study can be employed when designing microgrids to realize more stable systems.

Global mean square exponential stability and stabilization of uncertain switched delay systems with Lévy noise and flexible switching signals

This paper focuses on the stability analysis and stabilization problem for a class of uncertain switched delay systems with Lévy noise and flexible switching signals which unify the high-frequency switching and low-frequency switching. By employing the theory of switched systems, mathematical induction and stochastic analysis technique, some sufficient conditions in form of algebraic inequalities are derived to guarantee the stability and stabilization of such systems. Different from dwell time and average dwell time, the proposed switching rule constrained the partial dwell-time shows that the switching number in the same time interval can be more elastic. Finally, numerical examples are implemented to illustrate the effectiveness of the theoretical results.

On Boundedness of Solutions of State Periodic Systems: A Multivariable Cell Structure Approach

Many dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there are many classical techniques for analysis of boundedness and stability of such systems, most of these only permit to establish local properties. Motivated by this, a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented. The proposed method is inspired by the cell structure approach developed by Leonov and Noldus and characterized by two main advances. First, the conventional cell structure framework is extended to the case of dynamics, which are periodic with respect to multiple states. Second, by introducing the notion of a Leonov function, the usual definiteness requirements of standard Lyapunov functions are relaxed to sign-indefinite functions. Furthermore, it is shown that under (mild) additional conditions the existence of a Leonov function also ensures input-to-state stability, i.e., robustness with respect to exogenous perturbations. The performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system.

Self-Assembled Polymeric Membranes and Nanoassemblies on Surfaces: Preparation, Characterization, and Current Applications.

Biomembranes play a crucial role in a multitude of biological processes, where high selectivity and efficiency are key points in the reaction course. The outstanding performance of biological membranes is based on the coupling between the membrane and biomolecules, such as membrane proteins. Polymer-based membranes and assemblies represent a great alternative to lipid ones, as their presence not only dramatically increases the mechanical stability of such systems, but also opens the scope to a broad range of chemical functionalities, which can be fine-tuned to selectively combine with a specific biomolecule. Tethering the membranes or nanoassemblies on a solid support opens the way to a class of functional surfaces finding application as sensors, biocomputing systems, molecular recognition, and filtration membranes. Herein, the design, physical assembly, and biomolecule attachment/insertion on/within solid-supported polymeric membranes and nanoassemblies are presented in detail with relevant examples. Furthermore, the models and applications for these materials are highlighted with the recent advances in each field.

Fuzzy Control of Uncertain Positive Markov Jump Fuzzy Systems With Input Constraint.

This article considers the stochastic stability of uncertain positive Markov jump fuzzy systems (PMJFSs). The uncertainties consist of partially unknown membership functions and generally uncertain transition rates (GUTRs). In the GUTR model, each transition rate (TR) is completely unknown or only its estimate value is known. The coexistence of the partially unknown membership functions and GUTRs makes the control problem difficult to handle. Based on the T-S fuzzy scheme, a switching-type controller with input constraint which parallels as the structure of the uncertain fuzzy model is applied to ensure the positivity and stochastic stability of such systems. A linear decoupling strategy is proposed to tackle the coupling problems when designing the controller and further derives the desired controller parameters. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

The Immobilization of ChEMBL474807 Molecules Using Different Classes of Nanostructures

Indirubin derivatives and analogues are a large group of compounds which are widely and successfully used in treatment of many cancer diseases. In particular, the ChEMBL474807 molecule, which has confirmed inhibiting abilities against CDK2 and GSK3B enzymes, can be included in this group. The immobilization of inhibitors with the use of nanocarriers is an often used strategy in creation of targeted therapies. Evaluations were made of the possibility of immobilizing ligand molecules on different types of nanocarrier, such as carbon nanotubes (CNT), functionalized fullerene C60 derivatives (FF_X), and functionalized cube rhombellanes, via the use of docking methods. All results were compared with a reference system, namely C60 fullerene. The realized calculations allowed indication of a group of compounds that exhibited significant binding affinity relative to the ligand molecule. Obtained data shows that structural modifications, such as those related to the addition of functional groups or changes of structure symmetry, realized in particular types of considered nanostructures, can contribute to increases of their binding capabilities. The analysis of all obtained nano complexes clearly shows that the dominant role in stabilization of such systems is played by stacking and hydrophobic interactions. The realized research allowed identification of potential nanostructures that, together with the ChEMBL474807 molecule, enable the creation of targeted therapy.

Stability Analysis for State-constrained Switched Systems with All Subsystems Unstable

This paper mainly investigates the state constrained switched system with fully unstable subsystems. By limiting the state in a unit hypercube, a sufficient condition is derived to ensure the stability of such systems via a time-dependent strategy. The main idea is to use positive switching behavior to compensate state divergence caused by unstable states and setting a different ascend rate when state constraints occur or not. In order to make the conditions computable for a continuous-time switched systems with state constraints, the discretized Lyapunov Function method is applied, then a numerical example is given to show the practicability of the proposed method.

On stability analysis of nonlinear time-delay systems on time scales

This paper is concerned with the stability problems of a more general class of nonlinear time-delay systems, called time-scale time-delay systems, which can include not only the traditional continuous and discrete ones, but also some other cases, such as systems on hybrid time domains. As far as we know, the only existing approach for analyzing stability of such systems is the Razumikhin-type stability theorem. To enrich the stability results for such systems, this paper proposes the Lyapunov–Krasovskii theorem. Firstly, a conservative stability criterion is provided by requiring the time-scale time derivative of relating Lyapunov functional to be negative. Then, by introducing the time-scale type uniformly stable function and uniformly asymptotically stable function, a more relaxed stability theorem is proposed, in which the time-scale time derivative of Lyapunov functional is allowed to be non-negative. A numerical example about non-continuous and non-discrete time-delay systems is given to illustrate the effectiveness and general applicability of the theoretic results.

Quantized stabilization of stochastic systems with multiplicative noise under Markovian switching

A problem of quantized state feedback quadratic mean-square stabilization of discrete-time stochastic processes under Markovian switching and multiplicative noise is considered. A static quantizer is used in the feedback channel and the jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. It is shown that the coarsest quantization density that permits quadratic mean-square stabilization of this system is achieved with the use of a logarithmic quantizer, and the coarsest quantization density is determined by an algebraic Riccati equation, which is also the solution to a special linear stochastic Markovian switching control system. Also, sufficient conditions for exponential mean-square stabilization of such systems are also explored. An example is given to demonstrate the obtained results.

On the stability of inverse dynamics control of flexible-joint parallel manipulators in the presence of modeling error and disturbances

Inverse dynamics control is considered for flexible-joint parallel manipulators in order to obtain a good trajectory tracking performance in the case of modeling error and disturbances. It is known that, in the absence of modeling error and disturbance, inverse dynamics control leads to linear fourth-order error dynamics, which is asymptotically stable if the feedback gains are chosen to make the real part of the eigenvalues of the system negative. However, when there are modeling errors and disturbances, a linear time-varying error dynamics is obtained whose stability is not assured only by keeping the real parts of the frozen-time eigenvalues of the system negative. In this paper, the stability of such systems is investigated and it is proved that the linear time-varying system can be rendered stable by selecting the feedback gains such that the variation of the system becomes sufficiently slow. To illustrate the performance of the control method, deployment motion of a 3-RPR planar parallel manipulator subject to impact is simulated. For the impact model, the impulse-momentum and the coefficient of restitution equations for the system are derived.