Stability Analysis of Distributed-Order Hilfer–Prabhakar Systems Based on Inertia Theory

Mashoof, M.; Sheikhani, A. H. Refahi; Najafi, H. Saberi

doi:10.1134/s000143461807009x

Cited by 8 publications

(1 citation statement)

References 12 publications

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“…In the control theory, the stability analysis is one of the most important problems in the control of system including fractional derivatives. [1][2][3] From another general point of view, with the developments of theory of fractional calculus (integral and differential operations of non integer order) in the various fields of science and engineering, [4][5][6][7][8][9][10][11][12][13][14] the stability analysis of fractional dynamical systems has attracted increasing interest, and several methods have been introduced. [15][16][17][18][19][20] In the field of fractional-order control systems, the Lyapunov direct method is an available technique to analyze the stability and stabilization chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Stability and chaos control of regularized Prabhakar fractional dynamical systems without and with delay

Eshaghi

Ghaziani

Ansari

2019

Math Methods in App Sciences

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In this paper, we studied the stabilization of nonlinear regularized Prabhakar fractional dynamical systems without and with time delay. We establish a Lyapunov stabiliy theorem for these systems and study the asymptotic stability of these systems without design a positive definite function V (without considering the fractional derivative of function V is negative). We design a linear feedback controller to control and stabilize the nonautonomous and autonomous chaotic regularized Prabhakar fractional dynamical systems without and with time delay. By means of the Lyapunov stability, we obtain the control parameters for these type of systems. We further present a numerical method to solve and analyze regularized Prabhakar fractional systems. Furthermore, by employing numerical simulation, we reveal chaotic attractors and asymptotic stability behaviors for four systems to illustrate the presented theorem.

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