Polynomial Equations in Control Systems Design

Abstract

A control system design technique is presented for stochastic plants described by their rational transfer functions and by additive disturbances with rational spectral densities. The objective function is chosen as a linear combination of the plant input and output steady-state variances. The plant being controlled can be unstable and/or nonminimum-phase with improper transfer function. The design procedure yields a feedback controller, if one exists, and ensures the asymptotic stability of the closed-loop system.The approach presented here is based on polynomial equations. In fact, the design procedure is reduced to solving two linear polynomial equations whose unique solution directly yields the optimal controller as well as the corresponding value of the objective function. Apart from theoretical advantages, which include simple necessary and sufficient conditions for the optimal controller to exist, this approach is computationally attractive. All relevant algorithms are included to illustrate this important feature of the new design procedure.