Controller design with multiple objectives

This paper addresses the problem of synthesizing controllers that minimize the l₁ norm of the closed loop system subject to performance specifications expressed as linear constraints on the closed loop map. Convex constraints on the closed loop map, such as frequency point magnitude constraints, can be rewritten as an uncountable set of linear constraints. We use a previously derived duality result to approximate the convex constraint by a finite number of linear constraints and we derive bounds on the accuracy of the solutions of the approximate problems. The above mentioned duality result is also the basis for the analysis of the convergence properties of various computational methods.