State detection and stability for uncertain dynamical systems

In this paper, we study the problems of observer configuration and feedback stability for a certain class of uncertain dynamical systems whose nominal part is linear. Under some conditions on the nonlinear part, we show that the system is detectable and stabilizable by a continuous controller. A nonlinear observer can be designed provided that the system is detectable, that guarantees the observation error is globally exponentially stable. This observer design incorporates only the bound of the nonlinearities (uncertainties), and does not require exact knowledge concerning the structure of the plant nonlinearities. Furthemore, a continuous feedback control is proposed to exponentially stabilizes nonlinear dynamical systems using the Lyapunov approach, based on the stabilizability of the nominal system.