SIMULTANEOUS H-2 H(INFINITY) OPTIMAL-CONTROL - THE STATE-FEEDBACK CASE/

A simultaneous H-2/H(infinity) control problem is considered. This pro blem seeks to minimize the H-2 norm of a dosed-loop transfer matrix wh ile simultaneously satisfying a prescribed H(infinity) norm bound on s ome other closed-loop transfer matrix by utilizing dynamic state feedb ack controllers. Such a problem was formulated earlier by Rotea and Kh argonekar (Automatica, 27, 307-316, 1991) who considered only so calle d regular problems. Here, for a class of singular problems, necessary and sufficient conditions are established so that the posed simultaneo us H-2/H(infinity) problem is solvable by using state feedback control lers. The class of singular problems considered have a left invertible transfer function matrix from the control input to the controlled out put which is used for the H-2 norm performance measure. This class of problems subsumes the class of regular problems.