Non-fragile H∞ control of periodic piecewise time-varying systems based on matrix polynomial approach

This paper investigates the problem of non-fragile H-infinity control for periodic piecewise time-varying systems. Based on a Lyapunov function with continuous time-varying Lyapunov matrix polynomial, and combining with the positiveness and negativeness properties of matrix polynomials, the H-infinity performance analysis is first accomplished. Then consider two types of controller gain perturbations that are formulated by time-varying matrix parameters and norm-bounded uncertainties. The additive and multiplicative non-fragile controllers to guarantee the H-infinity performance of the system are formed, of which the controller gain could be solved with linear matrix inequalities directly. The designed non-fragile H-infinity controller is desirable in applications. Finally, numerical examples demonstrate the effectiveness of the proposed methods.