Balanced H∞ and H2 controllers

A balanced H_∞ controller is defined and analyzed in this paper. Gains of an H_∞ controller are obtained from the constrained solutions of two Riccati equations. If the solutions are equal and diagonal, the controller is H_∞ balanced. The transformation which generates the H_∞ balanced solution is derived. Also, properties of the balanced H_∞ controller, as well as its relationship to an H₂ balanced controller and to an open-loop balanced system, are presented. A characteristic property of flexible structures is that they have almost independent components in Moore balanced coordinates (1981). It is shown in this paper that the H_∞ balanced components are also almost independent and that the open-loop and the H_∞ balanced representations almost coincide. This property makes it possible to design reduced-order H_∞ controllers of comparable performance to full-order controllers.