Stabilization of nonlinear systems based on piecewise Lyapunov functions

This work presents a stabilization algorithm for piecewise approximated nonlinear systems based on piecewise Lyapunov functions. The stabilizing conditions are expressed in terms of bilinear matrix inequalities (BMIs). A large-scale BMI problem is decomposed in regional BMI problems. Connecting regional solutions of BMIs, we propose a design algorithm for a semi-global stabilizing controller. Some illustrated examples are given to show the validity of the proposed method.