Simultaneous [formula omitted] optimal control : The state feedback case

Abstract

A simultaneous H 2 H ∞ control problem is considered. This problem seeks to minimize the H 2 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 H 2 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 H 2 norm performance measure. This class of problems subsumes the class of regular problems.