Stabilization control of switched nonlinear system based on sum of square decomposition

The problem of feedback stabilization for a class of switched nonlinear systems is considered using polynomial Lyapunov function, and two methods are presented based on sum of square decomposition. The first is direct method and feedback controllers can be obtained by solving feasibility problem of sum of square program. The second method is iterative method and feedback controllers can be obtained by solving optimization problem of sum of square program. Both methods can be extended to the switched nonlinear systems with parameter uncertainty. A simulation example demonstrates the effectiveness of the presented methods.