Controllability of nonlinear fractional delay dynamical systems with prescribed controls
Articles
Xiao Li Li Ding
Xi’an Polytechnic University, China
Juan J. J. Nieto
Universidad de Santiago de Compostela, Spain
Published 2018-02-20
https://doi.org/10.15388/NA.2018.1.1
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Keywords

fractional delay dynamical systems
prescribed controls
controllability
Mittag–Leffler function
fixed point theorem

How to Cite

Ding, X.L.L. and Nieto, J.J.J. (2018) “Controllability of nonlinear fractional delay dynamical systems with prescribed controls”, Nonlinear Analysis: Modelling and Control, 23(1), pp. 1–18. doi:10.15388/NA.2018.1.1.

Abstract

In this paper, we consider controllability of nonlinear fractional delay dynamical systems with prescribed controls. We firstly give the solution representation of the fractional delay dynamical systems using Laplace transform and Mittag–Leffler functions. Then we give necessary and sufficient conditions for the controllability criteria of linear fractional delay dynamical systems with prescribed controls. Further, we use a fixed point theorem to establish the sufficient condition for the controllability of nonlinear fractional delay dynamical systems with prescribed controls. In particular, we determine several sufficient conditions on the nonlinear function term so that if the linear system is controllable, then the nonlinear system is controllable. Finally, we give two examples to demonstrate the applicability of our obtained results.

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