Consensus of fractional-order systems with non-uniform input and communication delays

2011 ◽  
Vol 226 (2) ◽  
pp. 271-283 ◽  
Author(s):  
J Shen ◽  
J Cao ◽  
J Lu
Keyword(s):  
Fractional Order ◽  
Great Influence ◽  
Sufficient Conditions ◽  
Communication Delays ◽  
Fractional Order Systems ◽  
Interaction Graph ◽  
Counter Example ◽  
Nyquist Stability ◽  
Input Delays ◽  
Frequency Domain Approach

This paper studies the consensus problems of fractional-order systems with non-uniform input and communication delays over directed static networks. Based on a frequency-domain approach and generalized Nyquist stability criterion, sufficient conditions are obtained to ensure the consensus of the fractional-order systems with simultaneously non-uniform input and communication delays. When the fractional-order [Formula: see text], it is found that the consensus condition is dependent on input delays but independent on communication delays. Surprisingly, when there is no input delay, consensus can be realized whatever the communication delays are. However, a counter-example shows that communication delays will have a great influence on the consensus condition when the fractional-order [Formula: see text]. Moreover, the bounds of input and communication delays are explicitly given to guarantee the consensus of the delayed fractional-order systems with fractional-order [Formula: see text] under an undirected interaction graph.

scholarly journals Admissibility of Fractional Order Descriptor Systems Based on Complex Variables: An LMI Approach

2020 ◽  
Vol 4 (1) ◽  
pp. 8
Author(s):  
Xuefeng Zhang ◽  
Yuqing Yan
Keyword(s):  
Fractional Order ◽  
Complex Plane ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
Fractional Order Systems ◽  
Lmi Approach ◽  
Numerical Examples ◽  
Necessary And Sufficient

This paper is devoted to the admissibility issue of singular fractional order systems with order α ∈ ( 0 , 1 ) based on complex variables. Firstly, with regard to admissibility, necessary and sufficient conditions are obtained by strict LMI in complex plane. Then, an observer-based controller is designed to ensure system admissible. Finally, numerical examples are given to reveal the validity of the theoretical conclusions.

scholarly journals Robust Stability and Stabilization of Interval Uncertain Descriptor Fractional-Order Systems with the Fractional-Orderα: The1≤α<2Case

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yuanhua Li ◽  
Heng Liu ◽  
Hongxing Wang
Keyword(s):  
Fractional Order ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Interval System ◽  
Interval Coefficients ◽  
Stability And Stabilization ◽  
Necessary And Sufficient ◽  
Robust Stability And Stabilization

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimensionnonly need to solve one 4n-by-4nLMI. Numerical examples are presented to shown the effectiveness of our results.

scholarly journals Modified Projective Synchronization between Different Fractional-Order Systems Based on Open-Plus-Closed-Loop Control and Its Application in Image Encryption

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongjuan Liu ◽  
Zhiliang Zhu ◽  
Hai Yu ◽  
Qian Zhu
Keyword(s):  
Fractional Order ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Order System ◽  
Coupling Scheme ◽  
Fractional Order Systems ◽  
Parameter Mismatch ◽  
Loop Control ◽  
Modified Projective Synchronization

A new general and systematic coupling scheme is developed to achieve the modified projective synchronization (MPS) of different fractional-order systems under parameter mismatch via the Open-Plus-Closed-Loop (OPCL) control. Based on the stability theorem of linear fractional-order systems, some sufficient conditions for MPS are proposed. Two groups of numerical simulations on the incommensurate fraction-order system and commensurate fraction-order system are presented to justify the theoretical analysis. Due to the unpredictability of the scale factors and the use of fractional-order systems, the chaotic data from the MPS is selected to encrypt a plain image to obtain higher security. Simulation results show that our method is efficient with a large key space, high sensitivity to encryption keys, resistance to attack of differential attacks, and statistical analysis.

scholarly journals SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL

2010 ◽  
Vol 20 (01) ◽  
pp. 81-97 ◽  
Author(s):  
ZAID M. ODIBAT ◽  
NATHALIE CORSON ◽  
M. A. AZIZ-ALAOUI ◽  
CYRILLE BERTELLE
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Dynamics ◽  
Sufficient Conditions ◽  
Linear Control ◽  
Fractional Order Systems ◽  
Control Laws ◽  
Response System ◽  
The Stability ◽  
Stability Results

The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived analytically to achieve synchronization of the chaotic fractional-order Chen, Rössler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis.

scholarly journals On the Stabilization and Observer Design of Polytopic Perturbed Linear Fractional-Order Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Omar Naifar ◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fractional Order ◽  
State Feedback ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Parameter Dependent ◽  
Lyapunov Technique

In this paper, the problem of stabilization and observer design of parameter-dependent perturbed fractional-order systems is investigated. Sufficient conditions on the practical Mittag–Leffler and Mittag–Leffler stability are given based on the Lyapunov technique. Firstly, the problem of stabilization using the state feedback is developed. Secondly, under some sufficient hypotheses, an observer design which provides an estimation of the state is constructed. Finally, numerical examples are provided to validate the contributed results.

scholarly journals Some Remarks on Estimate of Mittag-Leffler Function

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Jia Jia ◽  
Zhen Wang ◽  
Xia Huang ◽  
Yunliang Wei
Keyword(s):  
Dynamic Analysis ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Estimation Process ◽  
Made In

The estimate of Mittag-Leffler function has been widely applied in the dynamic analysis of fractional-order systems in some recently published papers. In this paper, we show that the estimate for Mittag-Leffler function is not correct. First, we point out the mistakes made in the estimation process of Mittag-Leffler function and provide a counterexample. Then, we propose some sufficient conditions to guarantee that part of the estimate for Mittag-Leffler function is correct. Meanwhile, numerical examples are given to illustrate the validity of the two newly established estimates.

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