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On the controllability of fractional dynamical systems

100%
Balachandran K., Kokila J.
International Journal of Applied Mathematics and Computer Science
|
2012
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tom 22
|
nr 3
523-531
EN
This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.
2
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Controllability of nonlinear implicit fractional integrodifferential systems

100%
Balachandran K., Divya S.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 4
713-722
EN
In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.
3
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Constrained controllability of nonlinear stochastic impulsive systems

100%
Karthikeyan S., Balachandran K.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 2
307-316
EN
This paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.
4
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Controllability of nonlinear stochastic systems with multiple time-varying delays in control

81%
Karthikeyan S., Balachandran K., Sathya M.
International Journal of Applied Mathematics and Computer Science
|
2015
|
tom 25
|
nr 2
207-215
EN
This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.
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