A time-varying output feedback controller for a class of nonlinear systems

This paper presents a solution for the design of a time-varying and parametric output feedback controller for a class of known nonlinear dynamic systems. The controller consists of two parts: a time varying nonlinear observer and a time-varying controller. Under a certain assumption on the nonlinear dynamics of the system, a stable and nonlinear time-varying observer can be firstly formulated. This observer can be logically combined with any pre-specified smooth nonlinear controller that uses the estimated state feedback with another tuning parameter so as to guarantee that the closed loop system state vector is uniformly bounded. 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. An extension to the stochastic system is also presented where the filtering design is made by looking at the minimized entropy of the error dynamics.