Asymptotic disturbance attenuation property analysis for discrete-time uncertain switched linear systems

In this paper, the disturbance attenuation properties in the sense of uniformly ultimate boundedness are investigated for a class of switched linear systems with parametric uncertainties and exterior disturbances. We aim to characterize the conditions under which the switched system can achieve a finite disturbance attenuation level. First, arbitrary switching signals are considered, and a necessary and sufficient condition is derived. Secondly, if the finite disturbance attenuation level is not preserved under arbitrary switchings, we restrict the switching signals so as to guarantee the finite disturbance attenuation levels. Two cases are considered here that depend on whether all the subsystems are uniformly ultimately bounded or not. For both cases, the switching signals are characterized by an average dwell time scheme. The techniques are based on multiple polyhedral Lyapunov and Lyapunov-like functions.