The impulsive property of switched singular systems and its stability

The problem of state jumps due to inconsistent initial conditions for impulsive and switched singular systems was addressed in this paper. The relationship between the solution with inconsistent initial condition and the one with consistent initial condition was discussed as well. The switched singular systems of each subsystem with different algebraic constraint conditions was modeled by switched singular systems with impulsive effects on switching instants. Multiple Lyapunov function approach for normal switched systems was extended to the impulsive and switched singular systems. A sufficient condition for the systems to be stable is given.