Design of decoupled multivariable stochastic control systems

In this paper, the problem of decoupling a linear time-invariant multivariable system subject to noise disturbances is investigated. Both plant and measurement noise are included. Under this setting, an optimal state feedback matrix is derived by minimizing a quadratic cost functional that overcomes the effects of the noise on the decoupling properties of the closed-loop system. This cost functional represents the tracking error between some desired output of a linear system driven by white noise and the actual closed-loop system subject to noise. An example is presented to illustrate the design approach.