Stability analysis of switched linear singular systems

This paper addresses the stability analysis problem for switched linear continuous-time singular systems. First, based on the equivalent dynamics decomposition form, a refined description for state jumps of the switched singular system is presented, which indicates that overall state jumps are resulted by two sequential state jumps. Second, sufficient conditions for exponential stability of the switched singular system with stable subsystems are presented. It is shown that the stability property of the system is completely determined by the switched reduced-order dynamic subsystem and the switching law induced state jumps. Then, a sufficient stability condition for the switched singular system with both stable and unstable subsystems is obtained. Finally, numerical examples are presented to illustrate the effectiveness of the proposed approach.