A parametric approach to the design of linear time-varying tracking controllers for nonlinear systems

In this paper the computation of linear time-varying tracking controllers on the basis of a Jacobian linearization of a nonlinear system about a reference trajectory is considered. An exponentially stabilizing controller is determined by approximately solving a Sylvester matrix differential equation using a Galerkin approach. The solution is obtained in parametric form so that conditions for the free parameters can be derived to assure exponential stability of the tracking error dynamics. The design procedure is demonstrated by computing a tracking controller for the stabilization of the side stepping of the inverted pendulum.