Control of switching systems under state and input constraints

We consider a particular class of hybrid systems characterized by a finite state machine and a set of discrete-time linear dynamical systems, each corresponding to a state of the machine. The hybrid control problem addressed consists of maintaining the output of the systems in a given subset of the output space, independently of the state of the FSM. Necessary and sufficient conditions are given for the existence of a solution and a constructive procedure is illustrated, based on the structure of the FSM.