Exponential Stability and Stabilization for Quadratic Discrete‐Time Systems with Time Delay

Abstract

In this note, we deal with the exponential stability and stabilization problems for quadratic discrete-time systems with time delay. By using the quadratic Lyapunov function and a so called 'Finsler's lemma', delay-independent sufficient conditions for local stability and stabilization for quadratic discrete-time systems with time delay are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.

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“…Then, the derivatives of V 1 (x) and V 2 (x) along the trajectory of System (44) are given as follows:…”

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