Disturbance attenuation and rejection for MIMO systems with stability degree constraint

This paper considers the optimal disturbance attenuation and rejection problem for MIMO systems affected by external sinusoidal disturbances based on stability degree constraint. The objective is to find an LQR optimal controller, by which the cost function minimum and the state with the optimal having a higher mean-square convergence rate can be obtained. A LQR control law is derive from a Riccati equation and Matrix equations. We give the existence and uniqueness conditions of the optimal control law. Finally, a practical example is given to illustrate the effectiveness of the theory.