On the controllability of fractional dynamical systems

Abstract

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.

The controllability of nonlinear implicit fractional delay dynamical systems

“…Several results on the controllability of nonlinear fractional dynamical systems with multiple delays and distributed delays in control were derived by Balachandran and Kokila (2012; as well as Balachandran et al (2012a;2012c). Recently, Balachandran and Divya (2014) studied the controllability of nonlinear implicit fractional integrodifferential systems.…”

Stabilizability of fractional dynamical systems

“…The problem of controllability of linear systems represented by fractional differential equations in finite dimensional spaces has been extensively studied by many authors [1,12,21]. Balachandran et al [6,7,8,9, 10] established sufficient conditions for the controllability of nonlinear fractional dynamical systems with or without delays in finite dimensional spaces using fixedpoint techniques. More recently, controllability of higher order nonlinear fractional dynamical systems are also studied by Balachandran et al [4,5].…”

Controllability criteria for time–delay fractional systems with a retarded state

“…The controllability of deterministic fractional dynamical systems without delays was studied, among others, by Klamka (2010;, Klamka et al (2014) or Babiarz et al (2016) for discrete-time fractional systems, Kaczorek (2011) as well as Kaczorek and Rogowski (2015) for positive fractional linear systems, both discrete-and continuous-time, and Chen et al (2006), Chikriy and Matichin (2008), Sakthivel et al (2011), Wang and Zhou (2012), Balachandran and Kokila (2012; or Balachandran et al (2012b) for continuous time fractional systems.…”