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A Delay-partitioning Approach to the Stability Analysis of 2-D Linear Discrete-time Systems with Interval Time-varying Delays

Dan Peng*, Jing Zhang, Changchun Hua, and Change Gao
International Journal of Control, Automation, and Systems, vol. 16, no. 2, pp.682-688, 2018

Abstract : "Two recent Lyapunov-based methods: delay-partitioning approach and Jensen inequality approach, have reduced the conservatism and the complexity of the stability result for one-dimensional (1-D) time-delay systems, respectively. This paper concerns the analysis of delay-dependent stability for two-dimensional (2-D) discrete systems with interval time-varying delays. By applying a delay partitioning-based Lyapunov function combining with the approaches of 2-D Jensen inequalities, a new delay-dependent stability criterion is derived in terms of linear matrix inequality (LMI). In addition to delay dependence, the obtained criterion is also dependent on the partition size. It is rigorously proved that the authors’ result reduces the conservativeness and computational burden than some recent ones. Numerical examples show the effectiveness and advantage of our result."

Keyword : "Delay-partitioning approach, delay-dependent, interval time-varying delays, linear matrix inequality (LMI), two-dimensional (2-D) discrete systems, 2-D Jensen inequalities."

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