Abstract

In this note, we deal with the stability and stabilization problems for quadratic systems with time delay. By using the quadratic Lyapunov function, Razumikhin-type techniques and a so called ‘Finslers lemma’, delay-independent sufficient conditions for local stability and local stabilization for quadratic time-delay systems 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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