Feedback control design of a switched system using non-common solutions of a quadratic minimization problem

In the present paper, a novel control design procedure for a switched system is proposed. The procedure is based on the guaranteed cost control and the quadratic performance index. A feedback control is designed to be close to the optimal linear quadratic feedback gains under the condition that the stability of the switched system is guaranteed. For this purpose, an iterative procedure is proposed in which the stability of the switched system is guaranteed by a common solution of simultaneous Lyapunov inequalities and the control performance is guaranteed by non-common solutions of linear matrix inequalities derived by the guaranteed cost control. The effectiveness of the proposed method is verified through numerical simulations.