Set Robust Control Invariance for Linear Discrete Time Systems

This paper introduces set robust control invariance, a concept that generalizes robust control invariance for systems described by difference equations to systems described by difference inclusions of special structure. The concept is useful for the analysis and synthesis of uncertain systems where a given control policy results in, for each initial state, a tube of trajectories rather than a sing trajectory; it also reveals the properties required for the terminal constraint set in receding horizon control of constrained linear systems with bounded disturbances and shows how improved terminal sets may be constructed. The family of set robust control invariant sets is characterized and the most important members of this family, the minimal and the maximal, are identified.