Relative controllability of fractional dynamical systems with delays in control

► The problem of controllability of fractional dynamical systems is investigated. ► Sufficient conditions for controllability are obtained. ► Fixed point theorems and the controllability Grammian matrix are used. This paper is concerned with the controllability of nonlinear fractional dynamical syst...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2012-09, Vol.17 (9), p.3508-3520
Main Authors: Balachandran, K., Zhou, Yong, Kokila, J.
Format: Article
Language:English
Subjects:
Computer simulation
Control systems
Controllability
Delay
Distributed delays
Dynamical systems
Fractional derivative
Mathematical analysis
Mathematical models
Mittag–Leffler function
Nonlinearity
Relative controllability
Time delays
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Summary:► The problem of controllability of fractional dynamical systems is investigated. ► Sufficient conditions for controllability are obtained. ► Fixed point theorems and the controllability Grammian matrix are used. This paper is concerned with the controllability of nonlinear fractional dynamical systems with time varying multiple delays and distributed delays in control defined in finite dimensional spaces. Sufficient conditions for controllability results are obtained using the Schauder fixed point theorem and the controllability Grammian matrix which is defined by Mittag–Leffler matrix function. Examples are provided to illustrate the theory.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2011.12.018