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On the componentwise stability of linear systems
Author(s) -
Pastravanu O.,
Voicu M.
Publication year - 2004
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.964
Subject(s) - exponential stability , mathematics , formalism (music) , stability (learning theory) , linear system , flow (mathematics) , nonlinear system , computer science , mathematical analysis , geometry , art , musical , quantum mechanics , visual arts , physics , machine learning
The componentwise asymptotic stability (CWAS) and componentwise exponential asymptotic stability (CWEAS) represent stronger types of asymptotic stability, which were first defined for symmetrical bounds constraining the flow of the state‐space trajectories, and then, were generalized for arbitrary bounds, not necessarily symmetrical. Our paper explores the links between the symmetrical and the general case, proving that the former contains all the information requested by the characterization of the CWAS/CWEAS as qualitative properties. Complementary to the previous approaches to CWAS/CWEAS that were based on the construction of special operators, we incorporate the flow‐invariance condition into the classical framework of stability analysis. Consequently, we show that the componentwise stability can be investigated by using the operator defining the system dynamics, as well as the standard ε−δ formalism. Although this paper explicitly refers only to continuous‐time linear systems, the key elements of our work also apply, mutatis mutandis , to discrete‐time linear systems. Copyright © 2004 John Wiley & Sons, Ltd.