scholarly journals Finite-time stability of $ q $-fractional damped difference systems with time delay

2021 ◽  
Vol 6 (11) ◽  
pp. 12011-12027
Author(s):  
Jingfeng Wang ◽  
◽  
Chuanzhi Bai
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Gronwall Inequality ◽  
The Novel ◽  
Delayed Systems ◽  
Finite Time Stability ◽  
Difference Systems ◽  
Grönwall Inequality ◽  
Uniqueness Of The Solution

<abstract><p>In this paper, we investigate and obtain a new discrete $ q $-fractional version of the Gronwall inequality. As applications, we consider the existence and uniqueness of the solution of $ q $-fractional damped difference systems with time delay. Moreover, we formulate the novel sufficient conditions such that the $ q $-fractional damped difference delayed systems is finite time stable. Our result extend the main results of the paper by Abdeljawad et al. [A generalized $ q $-fractional Gronwall inequality and its applications to nonlinear delay $ q $-fractional difference systems, J.Inequal. Appl. 2016,240].</p></abstract>

scholarly journals Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Pang Denghao ◽  
Jiang Wei
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Gronwall Inequality ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Generalized Gronwall Inequality ◽  
Grönwall Inequality

This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.

scholarly journals Finite-time stability of multiterm fractional nonlinear systems with multistate time delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
G. Arthi ◽  
N. Brindha ◽  
Yong-Ki Ma
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
The Novel ◽  
Finite Range ◽  
Time Stability ◽  
Finite Time Stability ◽  
Fractional System ◽  
The Stability

AbstractThis work is mainly concentrated on finite-time stability of multiterm fractional system for $0 < \alpha _{2} \leq 1 < \alpha _{1} \leq 2$ 0 < α 2 ≤ 1 < α 1 ≤ 2 with multistate time delay. Considering the Caputo derivative and generalized Gronwall inequality, we formulate the novel sufficient conditions such that the multiterm nonlinear fractional system is finite time stable. Further, we extend the result of stability in the finite range of time to the multiterm fractional integro-differential system with multistate time delay for the same order by obtaining some inequality using the Gronwall approach. Finally, from the examples, the advantage of presented scheme can guarantee the stability in the finite range of time of considered systems.

scholarly journals Finite time stability of linear fractional order dynam-ical system with variable delays

2018 ◽  
Vol 7 (2) ◽  
pp. 27
Author(s):  
Jackreece P. C ◽  
Aniaku S. E
Keyword(s):  
Dynamical System ◽  
Fractional Order ◽  
Finite Time ◽  
Gronwall Inequality ◽  
Sufficient Condition ◽  
Variable Delay ◽  
Time Stability ◽  
Finite Time Stability ◽  
Variable Delays ◽  
Grönwall Inequality

In this paper, some sufficient condition ensuring finite time stability are derived for a class of linear fractional order dynamical system with variable delay using generalized Gronwall inequality as well as classical Bellman-Gronwall inequality.

scholarly journals Finite-Time Stability of Solutions for Nonlinear q -Fractional Difference Coupled Delay Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jingfeng Wang ◽  
Chuanzhi Bai
Keyword(s):  
Finite Time ◽  
Gronwall Inequality ◽  
Delay Systems ◽  
Stability Of Solutions ◽  
Stability Criteria ◽  
Time Stability ◽  
Fractional Difference ◽  
Finite Time Stability ◽  
Grönwall Inequality

In this paper, we investigate and prove a new discrete q -fractional version of the coupled Gronwall inequality. By applying this result, the finite-time stability criteria of solutions for a class of nonlinear q -fractional difference coupled delay systems are obtained. As an application, an example is provided to demonstrate the effectiveness of our result.

scholarly journals Finite-Time Boundedness and Stabilization of Networked Control Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yeguo Sun ◽  
Jin Xu
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Finite Time ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Linear Matrix ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

The finite-time control problem of a class of networked control systems (NCSs) with time delay is investigated. The main results provided in the paper are sufficient conditions for finite-time stability via state feedback. An augmentation approach is proposed to model NCSs with time delay as linear systems. Based on finite time stability theory, the sufficient conditions for finite-time boundedness and stabilization of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.

scholarly journals An Improved Finite-Time Stability and Stabilization of Linear System with Constant Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Thaned Rojsiraphisal ◽  
Jirapong Puangmalai
Keyword(s):  
Time Delay ◽  
Linear System ◽  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Time Interval ◽  
State Variables ◽  
Time Stability ◽  
Finite Time Stability ◽  
Stability And Stabilization

Practical systems in engineering fields often require that values of state variables, during the finite-time interval, must not exceed a certain value when the initial values of state are given. This leads us to investigate the finite-time stability and stabilization of a linear system with a constant time-delay. Sufficient conditions to guarantee the finite-time stability and stabilization are derived by using a new form of Lyapunov-Krasovskii functional and a desired state-feedback controller. These conditions are in the form of LMIs and inequalities. Two numerical examples are given to show the effectiveness of the proposed criteria. Results show that our proposed criteria are less conservative than previous works in terms of versatility of minimum bounds and larger bounds of time-delay.

scholarly journals Stability of singular time-delay systems in the sense of non-Lyapunov: Classical and modern approach

2013 ◽  
Vol 67 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Dragutin Debeljkovic ◽  
Sreten Stojanovic ◽  
Marko Aleksendric
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Time Stability ◽  
Modern Approach ◽  
Finite Time Stability

This paper provides sufficient conditions for both practical stability and finite-time stability of linear singular continuous time-delay systems which can be mathematically described as Ex(t)=Aox(t)+A1x(t-t). Considering a finite-time stability concept, new delay independent and delay dependent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior. Moreover an linear matrix inequality (LMI) approach has been applied in order to get less conservative conditions.

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