Controllability of nonlinear fractional Langevin delay systems | Zendy

P. Suresh Kumar | Zendy; K. Balachandran | Zendy; N. Annapoorani | Zendy

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Controllability of nonlinear fractional Langevin delay systems

Author(s) -

P. Suresh Kumar,

K. Balachandran,

N. Annapoorani

Publication year - 2018

Publication title -

nonlinear analysis modelling and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.734

H-Index - 32

eISSN - 2335-8963

pISSN - 1392-5113

DOI - 10.15388/na.2018.3.3

Subject(s) - controllability , nonlinear system , control theory (sociology) , mathematics , dynamical systems theory , controller (irrigation) , gramian matrix , physics , computer science , control (management) , quantum mechanics , eigenvalues and eigenvectors , artificial intelligence , agronomy , biology

. In this paper, we discuss the controllability of fractional Langevin delay dynamical systems represented by the fractional delay differential equations of order 0 < α, β 6 1. Necessary and sufficient conditions for the controllability of linear fractional Langevin delay dynamical system are obtained by using the Grammian matrix. Sufficient conditions for the controllability of the nonlinear delay dynamical systems are established by using the Schauders fixed-point theorem. The problem of controllability of linear and nonlinear fractional Langevin delay dynamical systems with multiple delays and distributed delays in control are studied by using the same technique. Examples are provided to illustrate the theory.

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