Stability of Lurie Time-Varying Systems with Time-Varying Delay Feedbacks

Abstract

In this chapter, the stability problems of Lurie nonlinear system with time-varying plant and time-varying actuator under time-varying delay feedback are presented. First, absolute stability criteria, which we define as solvable matrix inequalities, are outlined by constructing a Lyapunov–Razumikhn functional. Second, we analyze these solvable matrix inequalities, and give their sufficient and necessary solvable conditions that are easily computed in practical systems. Third, based on our norm definition, solvable conditions and time-delay bound estimations can be obtained from two cases of solvable norm inequalities. More importantly, by analyzing all obtained procedures, we present the optimal combination method about a pair of \((\tau ,Q)\). Finally, an interested numerical example is presented to illustrate the above results effectively.