Disturbance attenuation properties for discrete-time uncertain switched linear systems

In this paper, we study a class of discrete-time switched linear systems affected by both parameter variations and additive l^∞ bounded disturbances. The problem of determining upper bounds on the l^∞ norm of the output is investigated. First, we study the condition under which the switched systems have finite l^∞ induced gain. Secondly, the l^∞ 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.