Proving Properties on PWA Systems Using Copositive and Semidefinite Programming

Abstract

In this paper, we present a model based on copositive programming and semidefinite relaxations of it to prove properties on discrete-time piecewise affine systems. We consider invariant i.e. properties represented by a set and formulated as all reachable values are included in the set. Also, we restrict the analysis to sublevel sets of quadratic forms i.e. ellipsoids. In this case, to check the property is equivalent to solve a quadratic maximization problem under the constraint that the decision variable belongs to the reachable values set. This maximization problem is relaxed using an abstraction of reachable values set by a union of truncated ellipsoids.