Relative controllability of linear systems of fractional order with delay

Therese  Mur; Hernan R.  Henriquez

doi:10.3934/mcrf.2015.5.845

Article Contents

2015, Volume 5, Issue 4: 845-858. Doi: 10.3934/mcrf.2015.5.845

This issue Previous Article Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation Next Article Stochastic recursive optimal control problem with time delay and applications

Relative controllability of linear systems of fractional order with delay

Therese Mur^1, and
Hernan R. Henriquez^1,

1.
Departmento de Matemática, Universidad de Santiago-USACH, Casilla 307, Correo-2, Santiago

Received: November 30, 2014

Revised: March 31, 2015

Published: November 2015

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Abstract

In this paper we are concerned with the controllability of control systems governed by a fractional differential equations with delay. Using the Mittag-Leffler function we define the concept of solution, and applying the properties of the Laplace transform we characterize the relative or pointwise controllability of the system. Our results generalize those of Kirillova and Churakova, which were established for first order systems. Finally, we show that functionally controllable fractional systems are rare.

Keywords:

Controllability of systems,
fractional differential equations,
retarded functional differential equations,
Mittag-Leffler function.

Mathematics Subject Classification: Primary: 93B05, 93C23; Secondary: 34A08, 26A33.

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