Robust H∞H∞ control for uncertain Lur’e systems with sector and slope restricted nonlinearities by PD state feedback

In this paper, the design of a PD controller for robust H∞H∞ stabilization of uncertain Lur’e systems with sector and slope restricted nonlinearities is considered. A PD controller is utilized to not only guarantee stability of systems but also reduce the effect of external disturbance to a H∞H∞ norm constraint. Sector bounds and slope bounds are used on a Lyapunov–Krasovskii functional through convex representation of the nonlinear function so that a less conservative H∞H∞ stability criterion is obtained. Using Finsler’s Lemma, the criterion is derived in terms of linear matrix inequalities (LMIs) that can be easily solved by various convex optimization techniques. Several examples show the effectiveness of the proposed methods.