We propose a fractional-order WINDMI system, as a generalization of an integer-order system developed by Sprott 2003 . The considered synchronization scheme consists of identical master and slave fractional-order WINDMI systems coupled by linear state error variables. Based on the stability theory of nonlinear fractional-order systems, linear state error feedback control technique is applied to...

The major contribution of this paper is to introduce the fractional calculus used to develop a fractional-order model for the DC electrical drive and, based on it, to design a fractional adaptive controller. In such a context, two modifications of the conventional Model Reference Adaptive Control theory are presented. Based on simulation results obtained in Matlab/ Simulink, the benefits of fra...

Parameter estimation for fractional-order chaotic systems has been an interesting and important issue in theory and various fields of application. In this paper, fractional orders, as well as systematic parameters of fractional-order chaotic systems are considered by treating fractional orders as additional parameters. The parameter estimation is transformed into a multidimensional optimization...

Grey system is a theory which specially studies poor information, and it possesses wide suitability. The parameters of multivariable grey FMGM(1,n) model with the fractional order accumulation can reflect the restricted and affected multi-variables relation with one another. We start by constructing background values based on vector continued fractions theory by using rational interpolation wit...

In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, standard approach from classical circuit theory applied. It includes realization system function by mathematical approximation desired phase response, and synthesis basic fractional-order (FO) one-port models as passive RC Cauer- Foster-form ...

Control and synchronization of the financial systems with fractional-order are discussed in this paper. Based on the stability theory of fractional-order differential equations, Routh-Hurwitz stability condition, and by using linear control, simpler controllers are designed to achieve control and synchronization of the fractional-order financial systems. The proposed controllers are linear and ...

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between ...

In this paper, it is considered that chaos synchronization of Chen fractional order time-delay chaotic systems and its application in secure communication. By use of the fractional calculus techniques, we find that chaos exists in the fractional order Chen system with time delays when the order is less than 3. Firstly, based on the Laplace transform theory, the conditions for achieving synchron...