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Equivalence of stability concepts for discrete time‐varying systems
Author(s) -
Bhaya Amit,
Das Francisco,
Mota Chagas
Publication year - 1994
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.4590040603
Subject(s) - equivalence (formal languages) , stability (learning theory) , mathematics , control theory (sociology) , computer science , pure mathematics , control (management) , artificial intelligence , machine learning
Stability concepts arising in the literature on absolute stability, difference inclusions and interval matrices are all shown to be equivalent to simultaneous asymptotic stability of a class of linear time‐varying discrete systems and, in turn, to exponential stability. This enables the classification of an interval matrix stability test due to Bauer et al. , a Lyapunov indicator test due to Barabanov and a constructive Lyapunov function test due to Brayton and Tong into a hierarchy of stability tests. Some applications of these tests are given and it is observed that they are not, in general, polynomial‐time tests.