Improved State Feedback Controller Synthesis for Piecewise-linear Systems

We propose a new technique for the design of state feedback controller for piecewise-linear systems, such that, the closed-loop systems are well-posed and asymptotically stable. First, a new criterion for the avoidance of sliding motion on the boundaries is presented. Then, the piecewise affine controller is constructed in a way such that the resulting closed-loop system satisfies the proposed criterion and a piecewise quadratic Lyapunov function can be used to establish the asymptotical stability. In this way, the control design problem is formulated as a numerical optimization problem under Linear Matrix Inequality constraints. The results are illustrated by application to control an aerobatic helicopter and balance an inverted pendulum on a cart, respectively, which demonstrates the efficacy and advantage of the proposed approach.