Explicit switching times and locations detection for linear hybrid systems

This paper is concerned with the exact calculus of the switching times for linear time invariant hybrid systems. We study the system's behavior that incorporates dynamical switches from a current location to another and propose an explicit procedure for a constructive treatment of the switching times. An implementable computational method elaborated in this paper makes it possible to solve the multidimensional problem of switching times detections in an algorithmic form. In this sense, the above numerical procedure also determines the sequence of locations of the hybrid system. Finally, we apply the proposed constructive approach to two illustrative examples.