Simultaneous H2 H∞ optimal control. The state feedback case

Abstract

A simultaneous H2 H∞ control problem is considered. This problem seeks to minimize the H2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H∞ norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (Automatica, 27, 307-316, 1991) who considered only so called regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneous H2 H∞ problem is solvable by using state feedback controllers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled output which is used for the H2 norm performance measure. This class of problems subsumes the class of regular problems. © 1993.