Controllability of fractional damped dynamical systems

Balachandran, K.; Govindaraj, V.; Rivero, Margarita; Trujillo, Juan J.

doi:10.1016/j.amc.2014.12.059

Cited by 55 publications

(28 citation statements)

References 32 publications

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“…We consider two types of non-linearities, Lipschitzian and non-Lipschitzian. For Lipschitzian nonlinearities are similar to those of [9] and [10]. Whereas the results concerning monotone nonlinearities are new in the theory of fractional order control systems.…”

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confidence: 65%

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Controllability of fractional dynamical systems: A functional analytic approach

Govindaraj¹,

George²

2017

Mathematical Control &Amp; Related Fields

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In this paper, we investigate controllability of fractional dynamical systems involving monotone nonlinearities of both Lipchitzian and non-Lipchitzian types. We invoke tools of nonlinear analysis like fixed point theorem and monotone operator theory to obtain controllability results for the nonlinear system. Examples are provided to illustrate the results. Controllability results of fractional dynamical systems with monotone nonlinearity is new.

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confidence: 65%

“…Since the linear system (3) is controllable, then, by Theorem 2.5, there exists a steering function P (t) for the linear system (3). If there exists x(t) satisfying (10), then the steering control for (1) is given by…”

Section: Definition 24 a Bounded Linear Operatormentioning

confidence: 99%

Controllability of fractional dynamical systems: A functional analytic approach

Govindaraj¹,

George²

2017

Mathematical Control &Amp; Related Fields

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“…Pinning-controllability analysis of complex networks and M -matrix approach is discussed by Song et al [30]. Balachandran et al [3][4][5]7] studied the relative controllability of fractional dynamical systems with multiple delay and distributed delay in control. A numerical method for delayed fractional-order differential equations is studied by Wang [32].…”

Section: Introductionmentioning

confidence: 99%

Controllability of nonlinear fractional Langevin delay systems

Kumar

Balachandran

Annapoorani

2019

NAMC

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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 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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“…Controllability results for fractional damped dynamical systems have been discussed in . The sufficient conditions have been obtained in for complete controllability of impulsive mixed type Volterra‐Fredholm stochastic systems with nonlocal conditions, and in existence results for impulsive neutral stochastic functional integro‐differential equations with infinite delay have been reported.…”

Section: Introductionmentioning

confidence: 99%

The Controllability of Fractional Damped Stochastic Integrodifferential Systems

Sathiyaraj

Balasubramaniam

2017

Asian Journal of Control

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In this paper, the complete controllability is investigated for nonlinear fractional damped stochastic integrodifferential system in finite dimensional space. Using linear controllability theory, sufficient conditions ensuring complete controllability are derived based on controllability Grammian matrix which is defined by Mittag‐Leffler matrix function and fixed‐point techniques. Finally, two numerical examples are given to verify the proposed conditions.

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Controllability of fractional damped dynamical systems

Cited by 55 publications

References 32 publications

Controllability of fractional dynamical systems: A functional analytic approach

Controllability of fractional dynamical systems: A functional analytic approach

Controllability of nonlinear fractional Langevin delay systems

The Controllability of Fractional Damped Stochastic Integrodifferential Systems

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