The existence of a common Lyapunov function for a class of linear switched descriptor systems was studied, where the system matrices were commute pairwise. We first presented work on two subsystems, a Lyapunov function was constructed and proved to be a common Lyapunov function of the system, and then we extended to the case of multi-subsytems, using the similar method. Finally, a sufficient condition for the existence of a common Lyapunov function for the linear switched descriptor system was presented, this assured the system asymptotically stable under arbitrary switching strategy.
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