Global Quadratic Stabilization of a Class of Nonlinear Systems

The problem of quadratic stabilization of a class of nonlinear systems will be examined in this paper. By employing a well-known Riccati approach, we develop a technique for designing a state feedback control law which quadratically stabilizes the system for all admissible uncertainties. This state feedback control law consists of linear and nonlinear feedback control terms. The linear feedback control term is generalized from a well-known H 1 result, while the nonlinear term can be viewed as a correcting term for the presence of nonlinear bounded uncertainty. This stabilization result is extended to static output feedback and to systems for which the nonlinear uncertainty satisses generalized matching conditions. Furthermore, we point out that in the presence of nonlinear uncertainty the global quadratic stability may be destroyed by some arbitrarily small mis-matched uncertainty in the input matrix, and proceed to establish the region of semi-global quadratic stability of the controlled system.