Performance analysis of Lur´e systems with time delays using linear matrix inequalities

This paper presents a novel analysis of the worst-case H_∞ performance for Lur´e systems with time delays (LSTD). The stability and performance analysis are based on the Lur´e-Postnikov Lyapunov function and the Lyapunov-Krasovskii functional. We apply a direct approach and an integral inequality to derive the sufficient condition for the stability of LSTD. As a result, the stability condition is delay-dependent, and can be formulated as convex optimization over linear matrix inequalities. Subsequently, the stability condition is extended to the worst-case H_∞ performance analysis of LSTD. In the numerical example, we show that the proposed sufficient conditions are less conservative than existing conditions.