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

This paper investigates the problem of non-fragile 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 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 performance of the system are formed, of which the controller gain could be solved with linear matrix inequalities directly. The designed non-fragile controller is desirable in applications. Finally, numerical examples demonstrate the effectiveness of the proposed methods.