Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Abstract

In this paper, we study the stability and performance optimization problem of discrete-time-varying polytopic systems with actuator saturation. First, the homogeneous polynomially parameter-dependent matrix function (HPP-DMF for abbreviation) is proposed. Then, a set invariance condition is obtained by applying the HPP-DMF to the Lyapunov function and gain scheduled control law. Based on the set invariance condition, an algorithm is proposed to minimize the worst-case performance. The conditions in the algorithm are expressed in terms of linear matrix inequalities (LMIs). In addition, it is shown that as the degree of the HPP-DMF increases the conditions become less conservative. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed technique.