Synthesis of low-order controllers for discrete LPV systems using LMIs and evolutionary search

A procedure for designing robust and gain-scheduled controllers for Discrete-time linear-parameter-varying (LPV) systems is proposed that exploits known bounds on the rate of parameter variation to reduce conservatism. Recent results on stability analysis of continuous-time LPV systems with known bounds on the rate of parameter change, using the concept of quadratic separators have been extended to compute a measure of worst-case performance of a discrete-time LPV system by solving an LMI problem. The problem of synthesizing robust and gain-scheduled controllers leads to a bilinear matrix inequality, and a hybrid approach to solving this problem based on LMI solvers and genetic algorithms is proposed in this paper. Two design examples illustrate the efficiency of the proposed method.