Disturbance decoupling with stability for impulsive switching linear systems

This paper deals with the problem of decoupling the output of a hybrid system from a disturbance input by means of a switching state feedback, which, at the same time, stabilizes, in a suitable sense, the compensated system. The class of hybrid systems considered consists of impulsive switching linear systems, that is switching linear systems whose state exhibits impulsive discontinuities, called jumps, at the switching instants. Switching is assumed to be time-driven and the distance between consecutive switching instants is assumed to be lower bounded by some positive number. Structural geometric methods and tools are used to investigate the decoupling problem and to study feedback stabilizability. Necessary and sufficient solvability conditions are given in the case in which the distance between consecutive switching instants can be assumed to be sufficiently large. A sufficient solvability condition is also provided in the case in which the lower bound for such distance is assigned.