Exponential Stability Analysis Research Articles

Exponential stability analysis of delayed memristor-based recurrent neural networks with impulse effects

In this paper, a generalized memristor-based recurrent neural network model with variable delays and impulse effects is considered. By using an impulsive delayed differential inequality and Lyapunov function, the exponential stability of the impulsive delayed memristor-based recurrent neural networks is investigated. Several exponential and uniform stability criteria of this impulsive delayed system are derived, which promotes the study of memristor-based recurrent neural networks. Finally, the effectiveness of obtained results is illustrated by two numerical examples.

New delay-range-dependent robust exponential stability criteria for uncertain linear systems with discrete interval and distributed time-varying delays and nonlinear perturbations

In this paper, we investigate the problem of robust exponential stability analysis for uncertain linear systems with discrete interval time-varying delay, distributed time-varying delay and nonlinear perturbations. Based on constructing an augmented Lyapunov–Krasovskii functional with some parameter, decomposition technique of coefficient matrix, mixed model transformation with Leibniz–Newton formula and utilization of zero equations, new delay-range-dependent robust exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the superiority of our results to those in the literature.

Exponential stability analysis and stabilization of switched delay systems

This paper investigates the problems of exponential stability analysis and stabilization for switched systems with time-varying delay via a new approach. To study the problems, the original system is transformed into an interconnection system, which is composed of a feedback subsystem and a forward one with a constant delay and an uncertainty disturbance. The exponential stability condition is presented to guarantee the α-input–output stability of the interconnection system based on the scaled small gain theorem, which is further proved to guarantee the exponential stability of the original system under arbitrary switching signal. Then the switching law existence condition is also proposed for exponential stabilization without input signal. Moreover, the problem of stabilization is further solved with admissible controllers obtained via convex optimizations. Both the problems are solved based on the model transformation method and the input–output approach. The merit of the proposed results lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the scaled small gain theorem. The superiority and effectiveness of our results over the existing ones are illustrated via some numerical examples.

Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

This paper is concerned with exponential stability analysis for linear continuous positive systems with bounded time-varying delay. Our approach is based on Lyapunov---Krasovskii functional with delay decomposition. The main idea is to divide uniformly the discrete delay interval into multiple segments and then to choose proper functionals with different weighted matrices corresponding to different segments. The synthesis of our delay-dependent sufficient stability criteria is formulated in terms of linear matrix inequalities. The proposed results are shown to be less conservative compared to other results from the literature. Some illustrative examples are given to show the effectiveness of the obtained results.

Implicit Lyapunov-Krasovski Functionals for Stability Analysis and Control Design of Time-Delay Systems

The method of Implicit Lyapunov-Krasovski Functional (ILKF) for stability analysis of time-delay systems is introduced. Theorems on Lyapunov, asymptotic, (hyper) exponential, finite-time and fixed-time stability analysis using ILKF are presented. The hyper exponential stabilization algorithm for a time-delay system is presented. The theoretical result is supported by numerical simulation.

A weak condition for global stability of delayed neural networks

The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function $V$ and on the strict negativity of the function $dV/dt$, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of $dV/dt $, nor do they require that the activation functions to be bounded or uniformly almost periodic.

Improved delay‐dependent exponential stability of singular systems with mixed interval time‐varying delays

This study deals with the problem of exponential stability analysis for a class of singular systems with interval time-varying discrete and distributed delays. By constructing a set of improved Lyapunov–Krasovskii functionals, new delay-dependent conditions are established in terms of linear matrix inequalities ensuring the regularity, impulse free and exponential stability of the system. This approach allows the authors to compute simultaneously the two bounds that characterise the exponential stability rate of the solution by various efficient convex optimisation algorithms. Numerical examples are given to illustrate the effectiveness of the obtained results.

Robust Exponential $$H_{\infty }$$ H ∞ Filtering for Discrete-Time Switched Fuzzy Systems with Time-Varying Delay

This paper considers $$H_{\infty }$$H? filtering of discrete-time uncertain switched nonlinear systems with time-varying delay via Takagi---Sugeno fuzzy model which is used to approximate each nonlinear subsystem. Fuzzy piecewise Lyapunov---Krasovskii functionals and average dwell time approaches are utilized for the exponential stability analysis and $$H_{\infty }$$H? filter design. A new sufficient condition is obtained to guarantee the exponential stability with a prescribed $$H_{\infty }$$H? performance index for the filtering error system. Filter parameter matrices can be obtained by solving sets of linear matrix inequalities. An example of an uncertain single-link robot arm is given to demonstrate the effectiveness of the proposed method.

Robustness analysis of global exponential stability of nonlinear stochastic systems with respect to neutral terms and time-varying delays

In this paper, we consider a class of nonlinear stochastic systems with respect to neutral terms and time-varying delays. Given a globally exponentially stable nonlinear stochastic system, the robustness of the global exponential stability of the system subject to a time delay and a neutral term can be derived by a subtle inequality and a transcendental equation. The upper bound of the allowable time delays and the neutral terms contraction coefficient is easy to verify and implement. Finally, an example with a numerical simulation is given to illustrate the presented criteria.

Pth Moment exponential stability of stochastic delayed hybrid systems with Lévy noise

In this paper, the problem of pth moment exponential stability analysis is considered for stochastic delayed hybrid systems with Lévy noise. By the technique of stochastic analysis as well as M-matrix theories, we propose some sufficient conditions to guarantee the exponential stability of the system. The criterion of mean square exponential stability for delayed neural networks with Lévy noise is derived as well. A numerical example is provided to show the usefulness of the proposed exponential stability criterion.

Delay-Dependent Stability Analysis for Uncertain Switched Time-Delay Systems Using Average Dwell Time

We are concerned with the stability problem for linear discrete-time switched systems with time delays. The problem is solved by using multiple Lyapunov functions to develop constructive tools for the exponential stability analysis of the switched time-delay system. Furthermore, the uncertainties of the switched systems are also taken into consideration. Sufficient delay-dependent conditions are derived in terms of the average dwell time for the exponential stability based on linear matrix inequalities (LMIs). Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

A Novel Approach to Robust Stability Analysis of Linear Time-Delay Systems

In this paper, we demonstrate that the Lyapunov-Krasovskii functional, which does not admit a quadratic lower bound, can be applied for the robust exponential stability analysis as well as for obtaining the exponential estimates for the solutions of linear time-invariant differential-difference systems with multiple delays.

Delay-Dependent Exponential Stability of Linear Time-Varying Neutral Delay Systems

In this paper, exponential stability analysis of linear time-varying neutral delay systems is considered. Based on fixed point theory, a necessary and sufficient condition for delay-dependent global exponential stability of such systems is derived. Eventually, the results are illustrated by two numerical examples.

New Delay-Range-Dependent Robust Exponential Stability Criteria of Uncertain Impulsive Switched Linear Systems with Mixed Interval Nondifferentiable Time-Varying Delays and Nonlinear Perturbations

We investigate the problem of robust exponential stability analysis for uncertain impulsive switched linear systems with time-varying delays and nonlinear perturbations. The time delays are continuous functions belonging to the given interval delays, which mean that the lower and upper bounds for the time-varying delays are available, but the delay functions are not necessary to be differentiable. The uncertainties under consideration are nonlinear time-varying parameter uncertainties and norm-bounded uncertainties, respectively. Based on the combination of mixed model transformation, Halanay inequality, utilization of zero equations, decomposition technique of coefficient matrices, and a common Lyapunov functional, new delay-range-dependent robust exponential stability criteria are established for the systems in terms of linear matrix inequalities (LMIs). A numerical example is presented to illustrate the effectiveness of the proposed method.

Network-based [formula omitted] filtering of parabolic systems

We design a network-based H∞ filter for a parabolic system governed by a vector semilinear N-D diffusion equation over a rectangular domain Ω under distributed in space measurements. The sampled in time measurements are sent to the observer over a communication network according to Round-Robin scheduling protocol (one after another in a periodic manner). The objective is to enlarge the sampling time intervals and, thus, to reduce the amount of communications, while preserving a satisfactory error system performance. We suggest to divide Ω into a finite number of rectangular sub-domains Ns, where stationary or mobile sensing devices provide spatially averaged state measurements to be transmitted through communication network. Sufficient conditions in terms of Linear Matrix Inequalities (LMIs) for the internal exponential stability and L2-gain analysis of the estimation error are derived via the time-delay approach to networked control systems. By solving these LMIs, the filter gain along with the upper bounds on the sampling time intervals, on the network induced time-delays, and on the diameters of the sub-domains can be found that preserve the internal stability of the error system and achieve a given L2-gain. Numerical examples illustrate the efficiency of the method.

Delay‐dependent exponential stability analysis of non‐linear switched singular systems with average dwell time approach

This manuscript analyzed the delay‐dependent stability problem for non‐linear switched singular time‐delay systems based on average dwell time and delay decomposition approach. Both cases of time‐delays namely constant and time‐varying delays are treated in the switched singular systems. Based on piecewise Lyapunov–Krasovskii functional, linear matrix inequality technique and an average dwell time approach, sufficient conditions which ensures that the delay‐dependent exponential stability conditions for uncertain switched singular systems are discussed. Finally, numerical examples and simulations are provided to demonstrate the effectiveness of the proposed techniques. © 2014 Wiley Periodicals, Inc. Complexity 21: 63–78, 2016

An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems

This paper addresses a novel global nonlinear sliding surface to achieve robustness and high performance for a class of uncertain nonlinear systems. Using the Lyapunov stability theorem, exponential stability analysis of the system states is proposed in the linear matrix inequality form. A new control law is designed to guarantee the elimination of the reaching phase and the existence of the sliding mode around the nonlinear surface right from the beginning. Two illustrative simulations are presented to demonstrate the robustness and effectiveness of the introduced design. It is worthwhile noticing that the proposed approach can be applied to a wide variety of uncertain nonlinear control problems.

Stability and passivity analysis of semilinear diffusion PDEs with time-delays

In the present paper, sufficient conditions for the exponential stability and passivity analysis of nonlinear diffusion partial differential equations (PDEs) with infinite distributed and discrete time-varying delays are derived. Such systems arise in many applications, e.g. in population dynamics and in heat flows. The existing Lyapunov-based results on the stability of diffusion nonlinear PDEs treat either systems with infinite delays or the ones with discrete slowly varying delays (with the delay-derivatives upper bounded by d< 1), where the conditions are delay-independent in the discrete delays. In this paper, we introduce the Lyapunov-based analysis of semilinear diffusion PDEs with fast-varying(without any constraints on the delay-derivative) discrete and infinite distributed delays. Two novel methods are suggested leading to conditions in terms of linear matrix inequalities. The first one provides delay-independent with respect to discrete delays stability criterion via combination of Lyapunov–Krasovskii functionals and of the Halanay inequality. Note that the Halanay inequality is not applicable to the passivity analysis. Therefore, the second method develops the direct Lyapunov–Krasovskii method via the descriptor approach that leads to delay-dependent (in discrete delays) conditions for the exponential stability and passivity. Numerical examples illustrate the efficiency of the methods.

A descriptor system approach to the delay-dependent exponential stability analysis for switched neutral systems with nonlinear perturbations

In this paper, the problem of exponential stability analysis for switched neutral systems with mixed time-delays and nonlinear perturbations based on descriptor system approach is addressed. Delay-dependent exponential stability results are derived in terms of linear matrix inequalities based on piecewise descriptor type Lyapunov–Krasovskii functional. Average dwell time approach is used to analyze switched neutral systems. In addition convex combination, delay decomposition and free-weighting matrix approaches have been employed to derive less conservative results. Further, numerical examples are illustrated to demonstrate the effectiveness and less conservativeness of the derived theoretical results.

Exponential Stability and Availability Analysis of a Complex Standby System

Abstract In this paper, we first investigate the solution of the two correlated units redundant system with two types of failure. By using the method of functional analysis, especially, the c0 semigroup theory of bounded linear operators on Banach space, we prove the well-posedness and the existence of positive solution of the system. By analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system. Finally, we analyze the reliability the system with the help of our main results and present some reliability indices of the system at the end of the paper.