A time-varying output feedback controller for nonlinear systems with linear output structure

This work presents a solution for the design of a time-varying and parametric output feedback controller for known general nonlinear dynamic systems subjected to linear output structure. The controller consists of two parts: an adaptive observer and a time-varying controller. Under a certain assumption on the nonlinear dynamics of the system, a stable and nonlinear adaptive observer can be firstly built This observer can be logically combined with any pre-specified smooth nonlinear controller that uses the estimated state feedback with another set of tuning parameters. A combined parameter dependent Lyapunov function is constructed and used to formulate an effective tuning rule for the time-varying parameters involved in both the observer and the control function. With this selection of the tuning rule, it has been shown that the closed loop system is stable. An example is included to illustrate the use of the proposed methods and encouraging results have been obtained.