Delay‐Dependent Stability Criterion for Discrete‐Time Systems with Time‐Varying Delays

Abstract

The stability analysis problem is considered for linear discrete‐time systems with time‐varying delays. A novel summation inequality is proposed, which takes the double summation information of the system state into consideration. The inequality relaxes the recently proposed discrete Wirtinger inequality and its improved version. Based on construction of a suitable Lyapunov‐Krasovskii functional and the novel summation inequality, an improved delay‐dependent stability criterion for asymptotic stability of the systems is derived in terms of linear matrix inequalities. Numerical examples are given to demonstrate the advantages of the proposed method.

A vehicle cloud control system considering communication quantization and stochastic delay

“…A similar idea was also adopted in some decentralized safety control like Bresch-Pietri and Del Vecchio [22], which used a predictive method to synchronize delayed system states. Apart from those probability-based methods, some studies [23,24] proposed less conservative LMI-based stability conditions for the constant-parameter linear feedback control system with time-varying but bounded feedback delay and system uncertainties. As those unreliable communication factors often happen concomitantly in practical systems, some research studied reliable control methods considering coupled conditions.…”