Mixed L∞/H∞ suboptimal controllers for SISO continuous-time systems

A successful controller design paradigm must take into account both model uncertainty and performance specifications. Model uncertainty can be addressed using the H_∞ robust control framework. This framework, however, cannot accommodate the realistic case where, in addition to robustness considerations, the system is subject to time-domain performance specifications. In this paper we present a design procedure for suboptimal L^∞ /H_∞ controllers. These controllers allow for minimizing the maximum amplitude of the time response due to a specified input, while, at the same time, addressing model uncertainty through bounds on the H_∞ norm of a relevant transfer function. The main result of the paper shows that suboptimal rational controllers can be obtained by solving a finite dimensional convex constrained optimization problem and a standard unconstrained H_∞ problem.