Deterministic characterization of a class of randomly switched systems and realization by pole sequences

An equivalence between the average behavior of a class of sequentially switched systems, defined herein, and the class of smooth time varying linear systems is obtained. The key in this is the notion of the nested pole sequence, a new definition for 'pole' in time varying systems. Realizations for the time variant systems are obtained directly from this nested pole sequence. A condition for the absence of a finite escape time is obtained, and various questions relating to the modeling and identification of these systems are reported. By the equivalence, these properties are also inherited by the switched systems.