Input‐to‐state stability for discrete‐time nonlinear impulsive systems with delays

Abstract

This paper aims to study the problem of input-to-state stability (ISS) for nonlinear discrete impulsive systems with time delays. Razumikhin-type theorems, which guarantee ISS -asymptotically ISS and exponentially ISS -for the discrete impulsive ones with external disturbance inputs, are established. As applications, numerical examples are given to illustrate the effectiveness of the theoretical results.

Constructions of ISS-Lyapunov functions for interconnected impulsive systems

“…In particular, σ can be chosen by σ (t) = Q(at), ∀t ≥ 0, for some a ∈ int(R n + ). (22) Proof: Take Ω-path σ as in (22). According to the Theorem 5 function V , defined by (18) is an ISS Lyapunov function.…”

“…Input-to-state stability of impulsive systems has been investigated in the papers [10], [5] (finite-dimensional systems) and [1], [15], [22] (time-delay systems). The stability of interconnected impulsive systems has been studied in [4].…”

On the pth moment integral input‐to‐state stability and input‐to‐state stability criteria for impulsive stochastic functional differential equations

“…Besides, Zhao et al obtained some results with respect to stochastic ISS criteria for switched stochastic systems. For the ISS of discrete‐time impulsive (stochastic) system, please refer to other works …”

pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

“…ISS property analysis of nonlinear systems with disturbance inputs is one of active research topics in modern nonlinear control theory. Therefore, it is of great significance to study ISS for impulsive systems, see, eg, other works …”

“…Most of the existing results pertain to the study of ISS property for continuous‐time impulsive systems, see other works and the references therein, but fewer studies the ISS property for discrete‐time impulsive systems . In addition, time delays occur frequently in many real‐world phenomena.…”