The Minimal Robust Positively Invariant Set for Linear Difference Inclusions and its Robust Positively Invariant Approximations

Abstract

Robust positively invariant (RPI) sets for linear difference inclusions are considered here under the assumption that the linear difference inclusion is absolutely asymptotically stable in the absence of additive state disturbances, which is the case for parametrically uncertain or switching linear discrete-time systems controlled by a stabilizing linear state feedback controller. The existence and uniqueness of the minimal RPI set and the minimal convex RPI set are studied. A new method for the computation of outer RPI approximations of the minimal RPI set for linear difference is presented; these approximations include a family of star–shaped RPI sets and two families of convex RPI sets. The use of a family of star–shaped RPI sets, and the characterization of the family, is reported for the first time. Keyword: Set invariance, Minimal Robust Positively Invariant Set, Linear Difference Inclusions

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Cite this paper

@inproceedings{Rakovic2005TheMR, title={The Minimal Robust Positively Invariant Set for Linear Difference Inclusions and its Robust Positively Invariant Approximations}, author={Sasa V. Rakovic and Konstantinos I. Kouramas and Eric C. Kerrigan and J. C. Allwright and David Q. Mayne}, year={2005} }