Generalized Kleinman-Newton method

Abstract

This paper addresses the general problem of optimal linear control design subject to convex gain constraints. Classical approaches based exclusively on Riccati equations or linear matrix inequalities are unable to treat problems that incorporate feedback gain constraints, for instance, the reduced-order (including static) output feedback control design. In this paper, these two approaches are put together to obtain a genuine generalization of the celebrated Kleinman-Newton method. The convergence to a local minimum is monotone. We believe that other control design problems can be also considered by the adoption of the same ideas and algebraic manipulations. Several examples borrowed from the literature are solved for illustration and comparison