Stabilization of a class of discrete-time hybrid systems with switchings: A set-theoretical approach

In this paper, the stabilization problems for a class of piecewise affine systems with mode-dependent dwell time switchings under state constraints and control constraints are investigated. The state feedback controllers, which are also piecewise affine and partition-dependent, are designed ensuring the positive invariance and contractivity of sets composed by constraints through linear programming approach. Consequently, by the invariance of reachable sets of the feasible region of each subsystem, the minimal mode-dependent dwell time is determined so as to guarantee asymptotic stability. A numerical example is given to show the validity and potential of the developed techniques.