Linear Complementarity Systems and Cone-Copositive Lyapunov Stability

Exponential stability of the origin of linear complementarity systems (LCS) is analyzed by applying Lyapunov theory. By representing the feasibility and the solution sets of the LCS as cones, a cone-copositive approach is used to get sufficient stability conditions expressed in terms of linear matrix inequalities (LMI). The proposed method is constructive in the sense that the solution of the set of LMI directly provides a quadratic Lyapunov function. Sufficient conditions for piecewise quadratic Lyapunov functions are obtained, as well. Illustrative examples show the effectiveness of the approach.