A cone-copositive approach for the stability of piecewise linear differential inclusions

In this paper a cone-copositive approach is proposed for investigating the stability of piecewise linear differential inclusions. From a different perspective the same issue can be viewed as the robust stability problem for uncertain piecewise linear systems. By using piecewise quadratic Lyapunov function the stability problem is formulated as a set of linear matrix inequalities each constrained into a specific cone, i.e. a set of cone-copositive programming problems. A procedure for solving the set of constrained inequalities is presented. The absolute stability problem for Lur´e systems with unknown feedback characteristic belonging to an asymmetric domain, is shown to be tractable as a particular case. Two examples are provided to show that the proposed approach might lead to less conservative estimation of the robust stability region with respect to the classical Circle criterion and to other approaches based on piecewise quadratic Lyapunov function.