Simultaneous ℋ∞ stabilization via fixed-order controllers: Equivalence and computation

This paper is concerned with simultaneous H_∞ stabilization with a fixed-order constraint on the controllers for multi-input/multi-output (MIMO) plants. By virtue of a new closed-loop stability and H_∞ performance characterization, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation. A convergent iterative algorithm is then provided to solve the condition, and a special property of the feasible solutions enables one to further improve the solvability via simple optimization on initial values. In addition, structural constraints on the controller gains or strong stabilizability can be incorporated into the design procedure in a straightforward manner.