Stability and invariance analysis of uncertain PWA systems based on linear programming

This paper analyzes stability of discrete-time uncertain piecewise-affine systems whose dynamics are defined on a bounded set χ that is not necessarily invariant. The objective is to prove the uniform asymptotic stability of the origin and to find an invariant domain of attraction. This goal is attained by defining a suitable extended dynamics (which is partially fictitious), and by using a numerical procedure based on linear programming. The theoretical results are based on the definition of a piecewise-affine, possibly discontinuous, Lyapunov function.