Finite-time stability in mean for Nabla Uncertain Fractional Order Linear Difference Systems

Fractals ◽  
2020 ◽  
Author(s):  
Qinyun Lu ◽  
Yuanguo Zhu ◽  
Bo Li
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Difference Systems ◽  
Linear Difference Systems

scholarly journals FTS and FTB of Conformable Fractional Order Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Abdellatif Ben Makhlouf ◽  
Omar Naifar ◽  
Mohamed Ali Hammami ◽  
Bao-wei Wu
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Conformable Fractional Derivative ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

scholarly journals Finite-Time Stability of Atangana–Baleanu Fractional-Order Linear Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jiale Sheng ◽  
Wei Jiang ◽  
Denghao Pang
Keyword(s):  
Linear System ◽  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Finite Time ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

This paper investigates a fractional-order linear system in the frame of Atangana–Baleanu fractional derivative. First, we prove that some properties for the Caputo fractional derivative also hold in the sense of AB fractional derivative. Subsequently, several sufficient criteria to guarantee the finite-time stability and the finite-time boundedness for the system are derived. Finally, an example is presented to illustrate the validity of our main results.

Input–output finite time stability of fractional order linear systems with 0 < α < 1

2015 ◽  
Vol 39 (5) ◽  
pp. 653-659 ◽  
Author(s):  
Ya-jing Ma ◽  
Bao-wei Wu ◽  
Yue-E Wang ◽  
Ye Cao
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Linear Time ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Input Output ◽  
Time Stability ◽  
Caputo Fractional Derivatives ◽  
Order Linear ◽  
Finite Time Stability

The input–output finite time stability (IO-FTS) for a class of fractional order linear time-invariant systems with a fractional commensurate order 0 < α < 1 is addressed in this paper. In order to give the stability property, we first provide a new property for Caputo fractional derivatives of the Lyapunov function, which plays an important role in the main results. Then, the concepts of the IO-FTS for fractional order normal systems and fractional order singular systems are introduced, and some sufficient conditions are established to guarantee the IO-FTS for fractional order normal systems and fractional order singular systems, respectively. Finally, the state feedback controllers are designed to maintain the IO-FTS of the resultant fractional order closed-loop systems. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

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.

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