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How scaling of the disturbance set affects robust positively invariant sets for linear systems
Author(s) -
Schulze Darup Moritz,
Schaich Rainer,
Can Mark
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3737
Subject(s) - scaling , invariant (physics) , computation , set (abstract data type) , mathematics , disturbance (geology) , lti system theory , control theory (sociology) , linear system , computer science , algorithm , control (management) , mathematical analysis , artificial intelligence , geometry , paleontology , mathematical physics , biology , programming language
Summary This paper presents new results on robust positively invariant (RPI) sets for linear discrete‐time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor, which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature. Copyright © 2017 John Wiley & Sons, Ltd.