Delay‐dependent Stability and Static Output Feedback Control of 2‐D Discrete Systems with Interval Time‐varying Delays

This paper is concerned with the problems of delay-dependent stability and static output feedback (SOF) control of two-dimensional (2-D) discrete systems with interval time-varying delays, which are described by the Fornasini-Marchesini (FM) second model. The upper and lower bounds of delays are considered. Applying a new method of estimating the upper bound on the difference of Lyapunov function that does not ignore any terms, a new delay-dependent stability criteria based on linear matrix inequalities (LMIs) is derived. Then, given the lower bounds of time-varying delays, the maximum upper bounds in the above LMIs are obtained through computing a convex optimization problem. Based on the stability criteria, the SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). With the use of the slack variable technique, a sufficient LMI condition is proposed for the BMI. Moreover, the SOF gain can be solved by LMIs. Numerical examples show the effectiveness and advantages of our results.

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