Time-varying controller for known nonlinear dynamic systems with guaranteed stability

This paper presents a solution for the design of a time-varying parametric controller for general nonlinear dynamic systems. The controller can be of any prespecified smooth nonlinear state feedback type so long as it includes a set of time-varying parameters. A Lyapunov function is constructed and used to formulate an effective tuning rule for the involved time-varying parameters. With this selection of the tuning rule, it has been shown that the closed loop system is stable. Two examples are included to illustrate the use of the proposed methods and encouraging results have been obtained.