Robust Control of Systems under Mixed Time/Frequency Domain Constraints via Convex Optimization

A successful controller design paradigm must take into account both model uncertainty and design specifications. Model uncertainty can he addressed using the ‘ H, or I 1 robust control theory. 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 tirne/frequency domain constraints and model uncertainty. This is achieved by minimizing a setinduced operator norm, subject to additional frequency domain performance specifications such as bounds on the ‘Hz or ‘ H, norm of relevant transfer functions. We show that this formulation results in a convex optimization problem that can be exactly solved. Thus, the conservatism inherent in some previous approaches is eliminated. We recently proposed [ 12-13] to approach time-domain COILstrained systems using an operator norm-theoretic approach. In this framework, robustness against model uncertainty and satisfaction of t imedomain constraints are achieved by minimizing a set induced operator norm, subject to additional frequency domain constraints. In this paper we generalize the framework of [12-131 by eliminating some of the approximations used there and by considering the more general case of output feedback controllers. The main result of the paper shows that for the case of ‘H2 or ‘ H, constraints, the resulting optimization problem can be cast into a finite-dimensional convex optimization form. This approach eliminates most of the conservatism inherent in previously proposed methods.