On the stabilization of linear discrete-time hybrid automata

The problem of stabilizing linear discrete-time hybrid automata is considered. A synthesis methodology is obtained by extending to hybrid systems the stabilization techniques based on stable convex combinations, originally developed for switching systems. The key idea is exploiting the underlying automaton structure by restricting the control actions to the ones corresponding to cycles in the automaton, which are identified using regular language tools. The so obtained system is equivalent to a regular switching system on which classical stabilization techniques can be applied. An algorithm to explore the candidate stabilizing controller actions is proposed and an application to an automotive engine control problem is described.