Iterative LMI approach to design robust state-feedback controllers for Lur'e systems with time-invariant delays

In this paper, we present a design of robust state-feedback stabilization and a design of robust state-feedback H (a) control for Lur'e systems with time-invariant delays and norm-bounded uncertainties. The criteria of state-feedback stabilization and state-feedback H (a) control are developed using Lyapunov-Krasovskii Theorem with a delay-partitioning Lyapunov-Krasovskii functional and an integral of sector-bounded nonlinearities. The design criteria are given in terms of bilinear matrix inequality, which is non-convex optimization. We develop algorithms based on coordinate optimization, which alternate between two LMI optimization problems, to solve for the robust state-feedback controllers. The proposed iterative LMI algorithm for H (a) control design is a local optimization procedure, but it can return satisfactory state-feedback controllers depending on the initialization. Numerical examples show that the proposed LMI algorithms can provide robust state-feedback stabilization to guarantee the closed-loop stability of LSTD and yield robust state-feedback control to guarantee the worstcase H (a) performance of the closed-loop LSTD.