Norm based robust control of state-constrained discrete-time linear systems

Most realistic control problems involve some type of constraint. However, to date, all the algorithms that deal with constrained problems assume that the system is perfectly known. On the other hand, during the last decade a considerable amount of time has been spent in the robust control problem. However, in its present form, the robust control theory can address only the idealized situation of completely unconstrained problems. In this note we present a theoretical framework to analyze the stability properties of constrained discrete-time systems under the presence of uncertainty and we show that this formalism provides a unifying approach, including as a particular case the well-known technique of estimating robustness bounds from the solution of a Lyapunov equation. These results are applied to the problem of designing feedback controllers capable of stabilizing a family of systems, while at the same time satisfying state-space constraints.