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

A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can be addressed using either H_∞ or L¹ robust control theory, depending upon the uncertainty characterisation. However, these frameworks cannot accommodate the realistic case where the design specifications include both time and frequency domain constraints. In this paper we present a design procedure for suboptimal L¹/H_∞ controllers. These controllers allows for minimizing the worst-case peak output due to bounded persistent disturbances, while, at the same time, satisfying an H_∞-norm constraint upon some closed-loop transfer function of interest. 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.