A linear-quadratic optimal solution to the decentralized servomechanism problem with robust noisy controllers

A linear-quadratic approach is presented to solve the robust decentralized servomechanism problem. It is assumed that not only the plant and the measurements, but the controllers may also be subject to certain disturbances. A physically meaningful quadratic cost function is defined, such that it is possible to assign desired weights to the errors, to their certain derivatives, to the system effort, and to the control efforts. It is shown that the resulting decentralized controlled system enjoys many properties like asymptotic tracking, stability, boundedness and robustness. The frequency domain characteristics of the resulting controllers are also discussed. It is shown that the solution does not require much control effort at high frequencies. Furthermore, the system is guaranteed not to have high frequency oscillations if certain design parameters are chosen properly.