LQR controller design of MIMO systems with external disturbances based on stability degree constraint

We consider an optimal control problem of MIMO systems affected by external disturbances with known dynamic characteristics but unknown initial conditions based on stability degree constraint. The objective is to find an optimal control, by which the cost function minimum and the state with the optimal control having a higher mean-square convergence rate can be obtained. A feedforward and feedback optimal control law is derived from a Riccati equation and a Matrix equation. We give the existence and uniqueness conditions of the feedforward and feedback optimal control law, and present an actualizing algorithm of solving the optimal control law. Finally, a practical example is given to illustrate the effectiveness of the theory.