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Strong practical stability and stabilization of uncertain discrete linear repetitive processes
Author(s) -
Dabkowski Pawel,
Galkowski Krzysztof,
Bachelier Olivier,
Rogers Eric,
Kummert Anton,
Lam James
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.812
Subject(s) - stability (learning theory) , mathematics , exponential stability , class (philosophy) , work (physics) , property (philosophy) , control theory (sociology) , stability conditions , linear matrix inequality , control (management) , discrete time and continuous time , mathematical optimization , computer science , nonlinear system , statistics , mechanical engineering , philosophy , epistemology , quantum mechanics , machine learning , artificial intelligence , engineering , physics
SUMMARY Repetitive processes are a distinct class of 2 D systems of both theoretical and practical interest. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass, respectively, where the former is a necessary condition for the latter. Recently applications have arisen where asymptotic stability is too weak, and stability along the pass is too strong for meaningful progress to be made. This, in turn, has led to the concept of strong practical stability for such cases, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality based tests, which then extend to allow robust control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that also extend to allow control law design. Copyright © 2011 John Wiley & Sons, Ltd.