Global Stability Criteria Research Articles

A note on the improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using twoʼs complement overflow arithmetic

This paper focuses on some critical issues in a recently reported approach [V. Singh, Improved LMI-based criterion for global asymptotic stability of 2-D state-space digital filters described by Roesser model using twoʼs complement overflow arithmetic, Digital Signal Process. 22 (2012) 471–475] for the global asymptotic stability of two-dimensional (2-D) fixed-point state-space digital filters described by the Roesser model employing twoʼs complement overflow arithmetic. In particular, it is highlighted that the situation where Singhʼs approach can be applied to ensure the global asymptotic stability of digital filters in the presence of twoʼs complement overflow nonlinearities is not conceivable. • We focus on critical issues in a recent approach for stability of 2-D digital filter. • It is hard to conceive any situation where the reported approach can be applied. • Implication of the approach in the context of 1-D digital filter is discussed.

Relaxed global asymptotic stability of 2-D state-space digital filters described by Roesser model with polytopic-type uncertainty

The problem of stability analysis of 2-D state-space digital filters described by Roesser model with parameter uncertainty is addressed in this paper. The underlying parameter uncertainty is modeled by a convex bounded (polytope type) uncertain domain. By applying both a new parameter-dependent Lyapunov function and a kind of matrix transformation technique, relaxed global asymptotic stability criteria of the 2-D state-space digital filters are proposed in terms of linear matrix inequalities (LMIs), which can be easily solved via standard numerical software. More importantly, the conservatism of the obtained global asymptotic stability criteria could be significantly reduced than existing ones. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

Stability analysis for impulsive stochastic fuzzy p-Laplace dynamic equations under Neumann or Dirichlet boundary condition

Under Neumann or Dirichlet boundary conditions, the stability of a class of delayed impulsive Markovian jumping stochastic fuzzy p-Laplace partial differential equations (PDEs) is considered. Thanks to some methods different from those of previous literature, the difficulties brought by fuzzy stochastic mathematical model and impulsive model have been overcome. By way of the Lyapunov-Krasovskii functional, Itô formula, Dynkin formula and a differential inequality, new LMI-based global stochastic exponential stability criteria for the above-mentioned PDEs are established. Some applications of the obtained results improve some existing results on neural networks. And some numerical examples are presented to illustrate the effectiveness of the proposed method due to the significant improvement in the allowable upper bounds of time delays.MSC:34D20, 34D23, 34B45, 34B37, 34K20.

Lipschitz stability criteria for functional differential systems of fractional order

In this paper, a class of fractional functional differential equations is investigated. Using differential inequalities and Lyapunov-like functions, Lipschitz stability, uniform Lipschitz stability, and global uniform Lipschitz stability criteria are proved. Since the problem of Lipschitz stability of dynamic systems is relevant in various contexts, including many inverse and control problem, our results can be applied in the qualitative investigations of many practical problems of diverse interest.

Global exponential stability of certain switched systems with time-varying delays

This paper is focused on global exponential stability of certain switched systems with time-varying delays. By using an average dwell time (ADT) approach that is different from the method in [P.H.A. Ngoc, On exponential stability of nonlinear differential systems with time-varying delay, Applied Mathematics Letters 25 (2012) 1208–1213], we establish a new global exponential stability criterion for the switched linear time-delay system under the ADT switching. We also apply this method to a general switched nonlinear time-delay system. A numerical example is given to show the effectiveness of our results.

M-matrix-based delay-range-dependent global asymptotical stability criterion for genetic regulatory networks with time-varying delays

This paper is concerned with the problem of global asymptotical stability for a class of delayed genetic regularity networks (GRNs), where the time delays belong to given intervals and assumed to be time-varying. By choosing an appropriate and novel Lyapunov functional and utilizing M-matrix theory, we derive an M-matrix-based delay-range-dependent sufficient condition under which the class of considered GRNs has unique nonnegative equilibrium point which is globally asymptotically stable. The sufficient condition given here is to check whether a constructed constant matrix is a nonsingular M-matrix. This can be easily done, since there are more than 50 equivalent conditions of nonsingular M-matrix, and hence the stability criterion obtained in this paper is different from existing ones in the form of linear matrix inequality (LMI). Finally, several examples and their simulations are presented to show the effectiveness of the proposed approach.

Stabilization of nonlinear systems with time-varying delays via impulsive control

In this paper, the stabilization for a class of nonlinear systems with time-varying delays is proposed via impulsive control. Using some analysis techniques such as reduction to absurdity, some new and useful criteria for global exponential stability are established. Furthermore, an example and some numerical simulations are presented to verify the effectiveness of the theoretical results.

The Role of Viral Infection on a Bacterial Ecosystem with Nutrient Enrichment

A mathematical analysis of a virus–marine bacteria interaction model is proposed to study the role of virus infection on a bacterial community in the presence of a nutrient. Our model includes four state variables, namely, nutrient concentration, susceptible bacteria biomass, infected bacteria biomass and phage virus concentration. The phage virus infection induces viral lysis, which releases into the marine environment on average \(b\) (viral replication factor) viruses per cell. The dynamical behavior of the system is studied by deriving the existence and bounded conditions and criteria for local and global stability of solutions. The local stability for the interior positive equilibrium is studied by using Routh–Hurwitz conditions. The general bifurcation analysis is shown. The qualitative behaviour of the system is verified through numerical simulation. It is observed that inclusion of nutrients in the system changes the nature of stability of different equilibria.

Master-slave synchronization of chaotic systems with a modified impulsive controller

This paper investigates global exponential synchronization of chaotic systems by designing a novel impulsive controller. The novel impulsive controller is a combination of current and past error states, which is a modification of the normal impulsive one. Some global exponential stability criteria are derived for the error system by utilizing the stability analysis of impulsive differential equations and differential inequalities and, moreover, the exponential convergence rate can be specified. An illustrative example is given to show the effectiveness of the modified impulsive control scheme.

A New Criterion for the Global Exponential Stability of Neural Networks with Time Delays

In this paper, we study the neural networks with time delays. By using of the Homeomorphism theory and employing an inequality, constructing a new Lyapunov-Krasovskill functional, we give a new sufficient condition, which is independent of the delays, guarantying the existence, uniqueness of the equilibrium point and it’s global exponential stable. Meanwhile, the incorrectness of calculation in the previous Refs is pointed out. We therefore improve the previous results.

Novel Global Exponential Stability Criterion for Recurrent Neural Networks with Time-Varying Delay

The problem of global exponential stability for recurrent neural networks with time-varying delay is investigated. By dividing the time delay interval [0,τ(t)] intoK+1dynamical subintervals, a new Lyapunov-Krasovskii functional is introduced; then, a novel linear-matrix-inequality (LMI-) based delay-dependent exponential stability criterion is derived, which is less conservative than some previous literatures (Zhang et al., 2005; He et al., 2006; and Wu et al., 2008). An illustrate example is finally provided to show the effectiveness and the advantage of the proposed result.

Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations

This paper is devoted to providing a novel method to global exponential stability of impulsive delayed differential equations. By utilizing relative nonlinear measure method, several global exponential stability criteria are presented for the impulsive delayed differential equations. Compared with the Razumikhin technique and Lyapunov function method, our method is less conservative and gives a convergence rate, and one of our stability criteria is more flexible by incorporating an adjustable matrix. An example and its simulation are provided to illustrate that our method is efficient and our results are new and correct.

Global Exponential Stability Criteria for Bidirectional Associative Memory Neural Networks with Time-Varying Delays

The global exponential stability for bidirectional associative memory neural networks with time-varying delays is studied. In our study, the lower and upper bounds of the activation functions are allowed to be either positive, negative, or zero. By constructing new and improved Lyapunov-Krasovskii functional and introducing free-weighting matrices, a new and improved delay-dependent exponential stability for BAM neural networks with time-varying delays is derived in the form of linear matrix inequality (LMI). Numerical examples are given to demonstrate that the derived condition is less conservative than some existing results given in the literature.

On the Role of Diffusion Behaviors in Stability Criterion forp-Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value

By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev spaceW01,p(Ω), a global asymptotical stability criterion forp-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinearp-Laplace diffusion item plays its role in the new criterion though the nonlinearp-Laplace presents great difficulties. Moreover, numerical examples illustrate that our new stability criterion can judge what the previous criteria cannot do.

Global Asymptotic Stability of a Neutral Stochastic Lotka-Volterra System

The work addresses a stochastic Lotka-Volterra system with delays of neutral type for which global asymptotic stability criteria are established.

Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays

This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results.

Synchronization stability in complex interconnected neural networks with nonsymmetric coupling

Some global stability criteria for arrays of linearly coupled delayed neural networks with nonsymmetric coupling are established on the basis of linear matrix inequality (LMI) method, in which the coupling configuration matrix may be arbitrary matrix with appropriate dimensions. Meanwhile, the relations of coupling matrix to stability and synchronization are discussed in detail, and some analysis methods to the synchronization stability of complex networks are also argued. The difficulty arising from the nonsymmetry of the coupling matrix has been overcome in this work. Numerical simulation is also given to verify the effectiveness of the theoretical results.

Stability of a class of switched stochastic nonlinear systems under asynchronous switching

The stability of a class of switched stochastic nonlinear retarded systems with asynchronous switching controller is investigated. By constructing a virtual switching signal and using the average dwell time approach incorporated with Razumikhin-type theorem, the sufficient criteria for pth moment exponential stability and global asymptotic stability in probability are given. It is shown that the stability of the asynchronous stochastic systems can be guaranteed provided that the average dwell time is sufficiently large and the mismatched time between the controller and the systems is sufficiently small. This result is then applied to a class of switched stochastic nonlinear delay systems where the controller is designed with both state and switching delays. A numerical example illustrates the effectiveness of the obtained results.

Global Asymptotic Stability Criteria of Bam Neural Networks with Time Delays

Global Asymptotic Stability Criteria of Bam Neural Networks with Time Delays

A Delay-Dependent Approach to Stability of Uncertain Discrete-Time State-Delayed Systems with Generalized Overflow Nonlinearities

This paper addresses the problem of global asymptotic stability of a class of uncertain discrete-time state-delayed systems employing generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. A new computationally tractable delay-dependent criterion for global asymptotic stability of such systems is presented. A numerical example is given to illustrate the effectiveness of the proposed method.