Linear robust control of dynamical systems with uncertainties bounded by nonlinear functions

It is shown that, if the nominal system is asymptotically stable and if the matching conditions are satisfied, a linear-type feedback control law will always stabilize a system with high-order nonlinear uncertainties in the states. It is also shown that the linear-type feedback control can locally stabilize the system if the matching conditions do not hold. Moreover, the stability region in which the linear type control works can be expanded to the whole state space if the nominal system can be stabilized with an arbitrarily large convergence rate. The controlled uncertain system is shown to be not only uniformly ultimately bounded but also asymptotically stable. These results are based on a theorem which generalizes previous results in Lyapunov stability theory