Passive control for Lur´e singularly perturbed systems with time-delay

In this paper, the absolutely stable and passive performance problem for Lur´e singularly perturbed systems with time-delay based on state feedback control is considered. First, the problem for the absolutely stable under passive performance constraint is studied in terms of Lyapunov stability theory. Second, a sufficient condition for the existence state feedback controller is presented, such that the resulting closed-loop system is absolutely stable. Furthermore, a problem for optimizing the stability perturbed upper bound is proposed based on solving a generalized eigenvalues problem of LMIs. Then an optimal state feedback controller can be obtained. Finally, a numerical example is provided to demonstrate the effectiveness and correctness of the proposed results.