Stability Analysis and Controller Synthesis for Parameter-Dependent Polynomial Nonlinear Systems

This paper addresses the stability analysis and state feedback synthesis for parameter-dependent nonlinear systems with polynomial vector fields. Based on the Lyapunov stability theorem, sufficient conditions to test the stability of the closed-loop system are presented and the synthesis problem of stabilizing feedback controller to enlarge the regions of attraction is converted to the optimization problem based sum of squares, which can be solved via semidefinite programming. A parameter-dependant Lyapunov function is adopted to reduce the conservativeness of the controller design.