Optimal ℋ∞-state feedback control for continuous-time linear systemsfeedback control for continuous-time linear systems

Abstract

This paper proposes a convex programming method to achieve optimal ℋ∞-state feedback control for continuous-time linear systems. State space conditions, formulated in an appropriate parameter space, define a convex set containing all the stabilizing control gains that guarantee an upper bound on the ℋ∞-norm of the closed-loop transfer function. An optimization problem is then proposed, in order to minimize this upper bound over the previous convex set, furnishing the optimal ℋ∞-control gain as its optimal solution. A limiting bound for the optimum ℋ∞-norm can easily be calculated, and the proposed method will achieve minimum attenuation whenever a feasible state feedback controller exists. Generalizations to decentralized and output feedback control are also investigated. Numerical examples illustrate the theory.