Observer-based adaptive stabilization of a class of uncertain nonlinear systems

In this paper, an adaptive output feedback stabilization method for a class of uncertain nonlinear systems is presented. Since this approach does not require any information about the bound of uncertainties, this information is not needed a priori and a mechanism for its estimation is exploited. The adaptation law is obtained using the Lyapunov direct method. Since all the states are not measurable, an observer is designed to estimate unmeasurable states for stabilization. Therefore, in the design procedure, first an observer is designed and then the control signal is constructed based on the estimated states and adaptation law with the σ-modification algorithm. The uniformly ultimately boundedness of all signals in the closed-loop system is analytically shown using the Lyapunov method. The effectiveness of the proposed scheme is shown by applying to a unified chaotic system.