PWA state feedback controller synthesis for piecewise-linear systems

We propose a new technique for the design of piecewise affine (PWA) state feedback controller for piecewise-linear systems (PWL) under the consideration of the possibility for sliding motion on the boundaries between the polytopic regions, which is less conservative than existing approaches in the literatures. Using piecewise quadratic Lyapunov function and a new criterion for the avoidance of sliding motion, the stabilization problem is formulated as a numerical optimization problem under Bilinear Matrix Inequality (BMI) constraints; We demonstrate the efficacy and advantage of the algorithm through a numerical example.