An improved exponential stability analysis method for discrete‐time systems with a time‐varying delay

Abstract

Exponential stability analysis of discrete‐time nonlinear systems with a time‐varying delay is concerned in this article. The main contribution of this article lies in proposing an improved stability analysis method called a delay‐mode‐based functional method. The improved method is presented by weakening a condition in the Lyapunov–Krasovskii functional method. With the help of the new method, less conservative exponential stability criteria of discrete‐time linear systems with a time‐varying delay are obtained and two classical examples are given to show that the delay‐mode‐based functional method is effective.

An Improved Stability Criterion for Discrete-Time Linear Systems With Two Additive Time-Varying Delays

“…R 2 > 0, R 4 > 0, R 2 > 0 and R 4 > 0 can be obtained from ( 7) and (8). Therefore, R 2 −, R 4 −, R 2 −, R 4 −, Z 2 − and Z 4 − dependent summation inequalities can be estimated based on lemma 2.…”

“…Thus, it is still conservative to some extent. How to enlarge the upper bound of the time delay to reduce the conservatism of the stability criterion is always a hot issue in control theory [8,9]. At present, most scholars focus on the delay-reliant stability conditions.…”

H∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

“…To reduce the conservatism of stability criteria, researchers have focused on developing suitable Lyapunov-Krasovskii functional (LKF) and establishing efficient approaches for estimating their direct differences. [11][12][13][14][15][16] Recently, several approaches have been explored to reduce the conservatism of stability criteria for discrete-time systems with TVD. They include the Jensen-based inequality (JBI), 17 the Wirtinger-based inequality (WBI), 18 and their extended forms.…”

“…Lyapunov stability theory and linear matrix inequality (LMI) technology have been widely used in most studies concerning the stability of time‐delay systems. To reduce the conservatism of stability criteria, researchers have focused on developing suitable Lyapunov–Krasovskii functional (LKF) and establishing efficient approaches for estimating their direct differences 11‐16 …”

Finite-time dissipative filter design for discrete-time stochastic interval systems with time-varying delays

“…[3][4][5] Furthermore, discretetime systems, especially discrete-time systems with time-varying delays, are expanded rapidly. [6][7][8] In recent years, some novel skills for the stability analysis of discrete-time systems with time-varying delays have been raised. For example, Zhang et al 9 have proposed the free-weighting-matrix method.…”