Robust control of systems under mixed time/frequency domain constraints via convex optimization

The authors propose to approach model uncertainty and time-domain constraints using an operator norm induced by the constraints to assess the stability properties of a family of systems. The proposed controller design method results in a convex optimization problem, where additional frequency-domain constraints can be imposed. It is shown that, when these additional constraints have the form of an H₂ or H_∞ bound, the resulting problem can be transformed into a finite-dimensional optimization and solved exactly. Thus, the conservatism inherent in some previous approaches is eliminated