A generalised time-varying output feedback controller for non-linear systems

This paper presents a solution for the design of a time-varying and parametric output feedback controller for known general non-linear 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 non-linear dynamics of the system, a stable and non-linear adaptive observer can be firstly built. This observer can then be logically combined with any pre-specified smooth non-linear controller that uses the estimated state feedback with a tuning parameter. 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 controller. With this selection of the tuning rule, it has been shown that the closed loop system is stable and the output can be controlled to converge to zero. An example is included to illustrate the use of the proposed methods and encouraging results have been obtained.