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Enhanced Stability Criteria for Discrete-time Systems with Time-varying Delay

Lijuan Zhu* and Chengyun Zhu
International Journal of Control, Automation, and Systems, vol. 19, no. 7, pp.2385-2394, 2021

Abstract : The stability problem of discrete-time linear systems with interval time-varying delays is investigated in this paper. According to the latest summation inequality technique, an improved free-matrix-based summation inequality is proposed in this paper. In order to make full use of the improved inequality to bound the upper bounds of the difference Lyapunov-Krasovskii functional (LKF), an augmented LKF with some extra status information is constructed. A new delay-range-dependent stability criterion is derived in the form of linear matrix inequalities (LMIs) via the modified LKF approach. The criterion is less conservative than some existing results. Finally, some standard numerical examples are presented the effectiveness of the proposed approach.

Keyword : Discrete-time system, linear matrix inequality, Lyapunov-Krasovskii functional, stability, time-varying delay.

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