In this paper, the exponential stability of singularly perturbed discrete systems (SPDSs) with time-delay is investigated via the Lyapunov’s direct method. In the previous results about the SPDS with time-delay, the asymptotic stability is obtained using the frequency-domain approach. However, we propose a composite Lyapunov function to show that the SPDS with time-delay is exponentially stable...

Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of...

This paper addresses the exponential stability problem for a class of discrete-time switched linear positive systems (DSLPSs) with time-delay. Firstly, an exponential stability criterion for a non-switched delay positive system is proposed. Then, by constructing a suitable co-positive type Lyapunov–Krasovskii functional, an exponential stability criterion for switched delay positive systems is ...

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability...

In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dep...

Stability of a switched system that consists of a set of linear time invariant subsystems and a periodic switching rule is investigated. Based on the Floquet theory, necessary and sufficient conditions are given for exponential stability. It is shown that there exists a slow switching rule that achieves exponential stability if at least one of these subsystems is asymptotically stable. It is al...

⎯By employing the Lyapunov stability theory and linear matrix inequality (LMI) technique, delaydependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory (BAM) neural networks with time-varying delays. The proposed condition can be checked easily by LMI control toolbox in Matlab. A numerical example is given to demonstrate the effectiveness...

This paper deals with almost sure and moment exponential stability of a class of predictorcorrector methods applied to the stochastic differential equations of Itô-type. Stability criteria for this type of methods are derived. The methods are shown to maintain almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions. A numerical experiment f...

Practical stability of real states of nonlinear sliding mode control systems is related to asymptotic vanishing of the corresponding sliding errors. Conditions are found such that, if the equivalent control achieves exponential stability, then real states are practically stable. In special cases, their exponential stability is obtained. A link between convergence of regularization procedures an...

In this paper, we mainly introduced a definition of moment exponential stability for multifactor uncertain differential equation. For illustrating of stability concept, several examples and counterexamples are given. Furthermore, a necessary and sufficient condition of stability in pth moment exponential of linear multifactor uncertain differential equation is obtained. Also, the necessary and ...