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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.

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