Tracking second-order dynamical systems

Output asymptotical tracking of a class of second-order dynamical systems based on decentralized state feedback control law is considered. The control law includes two parts, the controlled system state and the reference model state. First, the conditions for the existence of the solutions to the problem are given, which are two matrix equations, and one of them is second-order Sylvester matrix equation. Then complete parametric form of all controller gains is given. The algorithm for the model reference output tracking is concluded. This parametric method utilizes directly the original system data, so the method is simple and offers more convenience in control system designs. Simulations show the effectiveness of the proposed algorithm.