Optimal tracking control for MIMO systems with stability degree constraint subjected to sinusoidal disturbances

This paper considers the optimal tracking control (OTC) problem for MIMO systems affected by external disturbances based on stability degree constraint. The objective is to find an OTC, by which the cost function minimum and the state with the OTC having a higher mean-square convergence rate can be obtained. According to the special disturbance form, by supposing the Lagrange operator to solve the two-point boundary value (TPBV) problem, A feedforward and feedback OTC law is derived from a Riccati equation and Matrix equations. We give the existence and uniqueness conditions of the OTC law. Finally, a practical example is given to illustrate the effectiveness of the theory.