Simultaneous Stabilization and Robust Control of Polynomial Nonlinear Systems Using SOS Techniques

This technical note is concerned with the simultaneous stabilization and robust performance control for a class of polynomial nonlinear systems. Building on the tenets of state-dependent polynomial Lyapunov functions, we present sufficient conditions for simultaneous stabilization with and without Hinfin performance. These conditions can be verified by the recently developed sum of squares technique which essentially solves a linear matrix inequality feasibility problem.