New results on H2 suboptimal state feedback control with an H∞ constraint

In this paper, we consider an H₂ suboptimal control problem with H_∞ constraint. The problem is formulated as one of finding an internally stabilizing controller which achieves the prescribed H₂ norm of a closed-loop transfer matrix, subject to a constraint on the H_∞ norm of some other closed-loop transfer matrix. We give a sufficient condition for solving this problem. Moreover, using the result, we present a design algorithm for finding an internally stabilizing controller which achieves the H₂ performance better than the central H_∞ controller. It is assumed that the state of the plant is available for feedback.