Computing finitely reachable containable region for switching systems

In this paper the practical stability issue of a switching system is discussed in terms of solving a containability problem and an attraction problem. A novel computational procedure based on nonlinear programming is presented to compute a containable region, in which each trajectory from inside cannot move out under a given single-step-lookahead control policy. How to decide whether the obtained containable region is finitely reachable from a point outside the region is then examined. The proposed approach is demonstrated on a two-tank system.