A set induced norm approach to the robust control of constrained systems

Proposes an approach to time-domain constraints using an operator norm induced by the constraints to assess the stability properties of a family of systems. A robustness measure that indicates how well the family of systems under consideration satisfies a given set of constraints is introduced. The properties of this robustness measure for the case of additive parametric model uncertainty are explored, and it is shown that the proposed formalism provides a generalization of the well-known technique of estimating robustness bounds from the solution of a Lyapunov equation. A synthesis procedure for fixed order controllers, based on maximization of the robustness measure subject to additional performance constraints such as bounds on the control effort is proposed. It is shown that the proposed design procedure leads to a convex optimization problem