The Minimal Robust Positively Invariant Set for Linear Difference Inclusions and its Robust Positively Invariant Approximations
Rakovic S. V. and Kouramas K. I. and Kerrigan E. C. and Allwright J. C. and Mayne D. Q.
December 2005
Technical Report: Number: EEE/C&P/SVR/9-d/2005
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.
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BibTex Entry
- @TechReport{rakovic:kouramas:kerrigan:allwright:mayne:2005,
- author = {Rakovic S. V. and Kouramas K. I. and Kerrigan E. C. and Allwright J. C. and Mayne D. Q.},
- institution = {Imperial College London},
- title = {The Minimal Robust Positively Invariant Set for Linear Difference Inclusions and its Robust Positively Invariant Approximations},
- year = {2005},
- address = {Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK},
- bibkey = {rakovic:kouramas:kerrigan:allwright:mayne:2005},
- month = {December},
- note = {Number: EEE/C&P/SVR/9-d/2005}
- }
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