Asymptotically tracking in matrix second-order dynamical system framework

Model reference asymptotically tracking for a class of second-order dynamical systems in matrix second-order framework is investigated in this paper. A controller is used, which is composed of two parts: one is a state plus derivative feedback stabilizing controller, the other is a compensator, which compensates the effect of the reference model state to the tracking error. Based on a complete parametric solution to a class of second-order Sylvester matrix equations, the controller gains are completely parameterized. The original system data is directly used in the approach, and physical insight of the original problem is preserved. In the end a numerical example is given, and the simulations show the effect of the proposed parametric method.