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New Method for Absolute Stability of Delayed Lur'e Systems via Wirtinger-Based Lyapunov Function

This paper investigates the problems of absolute stability for Lur'e systems with time-varying delay and sector-bounded nonlinearity. Based on Wirtinger's inequality, a new Lyapunov functional named Wirtinger-based Lyapunov functional is constructed, in which some delay-dependent term and slack matrixes are introduced to refine the function. By using relaxed integral inequality to estimate the derivative of Lyapunov functional, less conservative stability criteria are achieved in terms of linear matrix inequalities (LMIs). The effectiveness and merits of derived conditions are verified by a numerical examples.