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Stability of switched linear discrete-time descriptor systems: A commutation condition

In this paper, we study stability of switched linear discrete-time descriptor systems. Under the assumption that all subsystems are stable and there is no impulse occurring at the switching instants, we establish a new pairwise commutation condition under which the switched system is stable. We also show that when the proposed commutation condition holds, there exists a common quadratic Lyapunov function (CQLΓ) for the subsystems. These results are natural and important extensions to the existing results for switched systems in the state space representation.