On Stabilization of Linear Switched Singular Systems via P-D State Feedback

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Impulsive phenomenon and state jumps at switching instants are inevitable control difficulties in the study of stability for switched singular systems. Proportional-derivative (P-D) state feedback may be an effective way to eliminate impulsive behaviors and state jumps. In this work, the problem of stabilization is studied for switched singular systems in the continuous-time case and discrete-time case. A synchronous design method of P-D state feedback controllers is proposed by introducing some free-weighting matrices. Based on P-D state feedback, some sufficient conditions, which can guarantee that the closed-loop systems are normal and stable (NS), are obtained by using multiple Lyapunov functions. Compared with step-by-step design, synchronous design brings more freedom to the design of P-D state feedback controllers and can better improve the dynamic performance of the systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.