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.

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.

Existence and finite-time stability of a unique almost periodic positive solution for fractional-order Lasota–Wazewska red blood cell models

2020 ◽  
Vol 13 (02) ◽  
pp. 2050013
Author(s):  
Yongkun Li ◽  
Yaolu Wang ◽  
Bing Li
Keyword(s):  
Blood Cell ◽  
Positive Solution ◽  
Fractional Order ◽  
Red Blood Cell ◽  
Finite Time ◽  
Time Interval ◽  
Almost Periodic ◽  
Cell Models ◽  
Time Stability ◽  
Finite Time Stability

In this paper, we are concerned with a class of fractional-order Lasota–Wazewska red blood cell models. By applying a fixed point theorem on a normal cone, we first obtain the sufficient conditions for the existence of a unique almost periodic positive solution of the considered models. Then, considering that all of the red blood cells in animals survive in a finite-time interval, we study the finite-time stability of the almost periodic positive solution by using some inequality techniques. Our results and methods of this paper are new. Finally, we give numerical examples to show the feasibility of the obtained results.

Finite time stability and comparison principles

1968 ◽  
Vol 64 (3) ◽  
pp. 749-756 ◽  
Author(s):  
A. A. Kayande ◽  
J. S. W. Wong
Keyword(s):  
Differential System ◽  
Finite Time ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Differential Inequalities ◽  
Finite Time Interval ◽  
Time Stability ◽  
Comparison Principles ◽  
Finite Time Stability

Motivated by discussion on practical stability in LaSalle and Lefschetz (3), Weiss and Infante (5), have discussed various notions of stability over finite time interval of a given differential system. This theory of stability differs from the usual stability theory mainly by the preassigned limits to which any given solution of the differential system must adhere. Sufficient conditions for these notions of stability are given in (5) in terms of certain Lyapunov-like functions satisfying some appropriate differential inequalities. The purpose of this article is to introduce some complementary notions of finite time stability and weaken the conditions on the differential inequalities involving Lyapunov-like functions by the use of comparison principles.

scholarly journals Robust finite-time stability of uncertain neutral nonhomogeneous fractional-order systems with time-varying delays

2020 ◽  
pp. 16-16
Author(s):  
Mihailo Lazarevic ◽  
Darko Radojevic ◽  
Stjepko Pisl ◽  
Guido Maione
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Test Procedure ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Stability ◽  
Extended Form ◽  
Finite Time Stability ◽  
Numerical Example

This article addresses the problem of finite-time stability for uncertain neutral nonhomogeneous fractional-order systems with time-varying delays where a stability test procedure is suggested. Based on the extended form of the generalized Gr?nwall inequality, a new sufficient condition for robust finite-time stability of such systems is established. Finally, a numerical example is given to show the effectiveness of the obtained result.

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