Exact Impulsive Observer with Predetermined Finite-Time Convergence of Fractional-Order Systems with Unknown Input

2018 ◽  
Author(s):  
Said Djennoune ◽  
Maamar Bettayeb ◽  
Ubaid Al-Saggaf
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Unknown Input ◽  
Fractional Order Systems ◽  
Finite Time Convergence

scholarly journals Finite-time stability of linear stochastic fractional-order systems with time delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lassaad Mchiri ◽  
Abdellatif Ben Makhlouf ◽  
Dumitru Baleanu ◽  
Mohamed Rhaima
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Finite Time ◽  
Stochastic Analysis ◽  
Fractional Order Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Analysis Techniques ◽  
Generalized Gronwall Inequality ◽  
Stability Of The Solution

AbstractThis paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for $\alpha \in (\frac{1}{2},1)$ α ∈ ( 1 2 , 1 ) . Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.

scholarly journals Finite Time Synchronization for Fractional Order Sprott C Systems with Hidden Attractors

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Cui Yan ◽  
He Hongjun ◽  
Lu Chenhui ◽  
Sun Guan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Engineering Practice ◽  
Fractional Order Systems ◽  
Spectral Entropy ◽  
Hidden Attractors ◽  
Finite Time Stability ◽  
Peculiar Phenomenon

Fractional order systems have a wider range of applications. Hidden attractors are a peculiar phenomenon in nonlinear systems. In this paper, we construct a fractional-order chaotic system with hidden attractors based on the Sprott C system. According to the Adomain decomposition method, we numerically simulate from several algorithms and study the dynamic characteristics of the system through bifurcation diagram, phase diagram, spectral entropy, and C0 complexity. The results of spectral entropy and C0 complexity simulations show that the system is highly complex. In order to apply such research results to engineering practice, for such fractional-order chaotic systems with hidden attractors, we design a controller to synchronize according to the finite-time stability theory. The simulation results show that the synchronization time is short and the robustness is stable. This paper lays the foundation for the study of fractional order systems with hidden attractors.

New Result on Finite-Time Stability of Fractional-Order Nonlinear Delayed Systems

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Liping Chen ◽  
Wei Pan ◽  
Ranchao Wu ◽  
Yigang He
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Lyapunov Method ◽  
Time Interval ◽  
Fractional Order Systems ◽  
Finite Time Interval ◽  
Time Stability ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Delayed System

Since Lyapunov method has not been well developed for fractional-order systems, stability of fractional-order nonlinear delayed systems remains a formidable problem. In this letter, finite-time stability of a class of fractional-order nonlinear delayed systems with order between 0 and 1 is addressed. By using the technique of inequalities, a new and simple delay-independent sufficient condition guaranteeing stability of fractional-order nonlinear delayed system over the finite time interval is obtained. Numerical examples are presented to demonstrate the validity and feasibility of the obtained results.

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