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Controllability and stabilizability of linear time‐varying distributed hereditary control systems
Author(s) -
Henríquez Hernán R.,
Prokopczyk Andréa
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3219
Subject(s) - controllability , mathematics , semigroup , control theory (sociology) , operator (biology) , exponential stability , linear system , stability (learning theory) , property (philosophy) , control (management) , mathematical analysis , computer science , biochemistry , chemistry , physics , philosophy , epistemology , repressor , nonlinear system , quantum mechanics , artificial intelligence , machine learning , transcription factor , gene
This paper is concerned with the controllability and stabilizability problem for control systems described by a time‐varying linear abstract differential equation with distributed delay in the state variables. An approximate controllability property is established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operators associated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptotic stability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximate controllability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes the system. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley & Sons, Ltd.