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Robust exponential stability of time‐varying linear systems
Author(s) -
Hinrichsen D.,
Pritchard A. J.
Publication year - 1993
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.4590030105
Subject(s) - control theory (sociology) , robustness (evolution) , nonlinear system , bounded function , linear system , scalar (mathematics) , upper and lower bounds , mathematics , exponential stability , stability (learning theory) , exponential function , computer science , mathematical analysis , physics , control (management) , geometry , quantum mechanics , artificial intelligence , machine learning , gene , biochemistry , chemistry
This paper investigates the robustness of time‐varying linear systems under a large class of complex time‐varying perturbations. Previous results 8 which were restricted to bounded linear perturbations of output feedback type are generalized to unbounded and nonlinear perturbations of multi‐output feedback type. We establish a lower bound for the stability radius of these systems and show how it may be possible to improve the bound using time‐varying scalar transformations of the state, input and output variables. The results are applied to derive Gershgorin type stability criteria for time‐varying linear systems.