Disturbance attenuation property for a class of uncertain discrete-time linear switching systems

In this paper, a subclass of switching systems is considered, which is the discrete-time linear switching systems with only in-loop transitions. In the presence of parameter variations and additive l^∞ bounded disturbances, the control problem solved consists of determining the non-conservative bounds on the l^∞ norm of the controlled output, independently of the external uncontrollable event and uncertainties. The basic idea employed in this paper is to translate the required level of performance into the constraint on the controlled switching systems, then this constraint is considered as the safety problem for this class of switching systems. Together with the bisection method, the optimal level of performance that solves the disturbance attenuation property problem can be approximated. At last, some simulation results are included to show the applicability of the technique.