Mixed L1/H∞ controllers for MIMO continuous-time systems

A successful controller design paradigm must be able to handle multiple, and often conflicting, design specifications. In this paper we present a design procedure for suboptimal L¹/H_∞ controllers. These controllers allow for minimizing the L¹ norm of the closed-loop transfer function between a pair of signals, while satisfying an H_∞-norm constraint upon a different closed-loop transfer function. Thus, they can be thought of as achieving nominal performance in terms of disturbance rejection, while guaranteeing robust stability. The main result of the paper shows that rational mixed L¹/H_∞ suboptimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a standard, unconstrained H_∞ problem