Robust Non-fragile Guaranteed Cost Control of Continuous-Time Piecewise-Affine Systems with Norm-Bounded Uncertainties

Abstract

In this paper, the problem of designing robust non-fragile guaranteed cost state feedback controller for a class of continuous-time singular piecewise-affine systems is considered. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, the robust non-fragile stabilization condition is established, and meanwhile, the condition of constructing non-fragile guaranteed cost state feedback controller is proposed. Under the multiplicative perturbation, the design method of robust non-fragile stabilization controller is given in terms of the feasible solutions of linear matrix inequalities. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Finally, numerical examples are given to illustrate the effectiveness of the proposed design methods.