Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, December 9-12, 2003.

Abstract -- In this paper, we study a class of discrete-time switched linear systems affected by both parameter variations and additive l1 bounded disturbances. The problem of de-termining
upper bounds on the l1 norm of the output is investigated. First, we study the condition under which the switched systems have finite l1 induced gain. Secondly, the l1 induced gain is calculated for such switched system under arbitrary switching signals. Thirdly, we answer the question whether there exists proper switching mechanism for such switched system to achieve a given disturbance attenuation level. The techniques are based on positive invariant set theory.

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