Minimax control under a bound on the partial covariance sequence of the disturbance

Abstract

A discrete-time linear SISO plant that is acted on by a stochastic disturbance is considered. It is assumed that a restriction on the partial covariance sequence of the disturbance is given. The cost function is a maximum of the closed-loop system output variance over the class of disturbances. The problem is to find the optimal linear stabilizing regulator. The transfer function of the optimal closed-loop system is constructed in explicit form. It is shown that the minimax regulator is intermediate between the H ∞ and H 2 optimal regulators. As a result of the problem solution, generalizations of the Caratheodory-Fejer and Nevanlinna-Pick theorems are obtained.