Robust control of systems with both norm-bounded and nonlinear uncertainties

The robust stabilization problem for a class of systems with both norm-bounded and nonlinear uncertainties is considered. The nonlinear uncertainty is assumed to satisfy a matching condition but the norm-bounded one may not. By generalizing an H_∞ control result, the authors develop a Riccati equation technique for designing state feedback control to globally exponentially stabilize the system for all admissable uncertainties. This stabilization result is then extended to static output feedback and to systems for which the nonlinear uncertainty satisfies a generalized matching conditions. Furthermore, the authors point out that the global stability in the presence of nonlinear uncertainty may be destroyed by some arbitrarily small mismatched uncertainty in the input matrix, and proceed to establish the region of semi-global exponential stability of the controlled system