Stability analysis of discrete-time systems with time-varying delay via a delay-dependent matrix-separation-based inequality✩

This paper is concerned with the stability analysis of discrete-time systems with a time-varying delay. Different from the recent related works that reduce the conservatism by increasing the complexity of Lyapunov functions, this paper aims at conservatism-reduction by using relatively simple Lyapunov functions with an augmented double summation term. The key point for achieving this task is that a delay-dependent matrix-separation-based inequality is established to estimate the augmented-type summation term arising in the forward difference of Lyapunov functions. The proposed method provides a general form of inequalities, which realizes the effective reduction of estimation gap, and also introduces several tractable delay-dependent matrices, which achieves the full use of available delay-related information. As a result, for two types of time-varying delays, the usage of the proposed inequality under different separations leads to two less conservative and low complex stability criteria, whose advantages are demonstrated via three examples.