Adaptive control design for piecewise-linear differential inclusion with parameter uncertainty

This paper presents Lyapunov-based adaptive control method for piecewise-linear differential inclusions {PWLDI} with parameter uncertainty. The basic idea of the proposed approach is to construct a piecewise control law and a parameter adaptive law for the PWLDI in a way such that a piecewise quadric Lyapunov function can be used to establish the global stability and H_∞ performance of the resulted closed-loop systems. All the synthesis conditions can be formulated as an optimization problem subjected to a set of Bilinear Matrix Inequalities {BMIs}. Finally we demonstrate the efficiency of the algorithm through an example.