Mixed L/sup 1//H/sub /spl infin// 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/sub /spl infin// or L/sup 1/ 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 L/sup 1//H/sub /spl infin// controllers. These controllers allows for minimizing the worst-case peak output due to bounded persistent disturbances, while, at the same time, satisfying an H/sub /spl infin//-norm constraint upon some closed-loop transfer function of interest. The main result of the paper shows that rational mixed L/sup 1//H/sub /spl infin// 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/sub /spl infin// problem.