Robust state-feedback controllers for systems under mixed time/frequency domain constraints

A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can be addressed using H_∞ or l₁ robust control theory, depending upon its characterisation. However, these frameworks cannot accommodate the realistic case where the design specifications include both time and frequency-domain constraints. In this paper we propose an approach that takes explicitly into account both mixed time/frequency-domain constraints and model uncertainty. This is achieved by minimising an upper bound of a set-induced operator norm, subject to additional frequency-domain specifications such as bounds on the H₂ and H_∞-norm of relevant transfer functions. The main result of the paper shows that, by using the parametrization proposed by Kaminer (1993), the problem can be cast into a finite-dimensional, differentiable convex optimisation problem, that can be solved by using gradient-based methods. This theory is illustrated with an application to the lateral dynamics of a B767 aircraft