A tracking controller for linear time-varying systems

This paper proposes a new tracking control design for linear time-varying systems. The proposed control input, which is in the span of finitely many preselected input data, minimizes the L(2)-norm of the output tracking error. The more input data is used, the less L(2)-norm of the tracking error is achieved. The design of the new controller, which consists of a feedforward controller and a discretized state feedback loop, requires affinite-time preview of the system parameters and the reference trajectory. It is shown that as long as the preview time is longer than a critical value, the closed-loop stability is maintained irrespective of the stability property of the system's zero dynamics. When the system parameters are periodically time-varying, the pro posed design can be solely based on a set of experimental input and output data instead of on the exact information of system parameters.