Passivity Analysis of Fractional-Order Neural Networks with Interval Parameter Uncertainties via an Interval Matrix Polytope Approach

2022 ◽  
Author(s):  
Shasha Xiao ◽  
Zhanshan Wang ◽  
Changlai Wang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Interval Matrix ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Passivity Analysis

scholarly journals Improved Results on Finite-Time Passivity and Synchronization Problem for Fractional-Order Memristor-Based Competitive Neural Networks: Interval Matrix Approach

2022 ◽  
Vol 6 (1) ◽  
pp. 36
Author(s):  
Pratap Anbalagan ◽  
Raja Ramachandran ◽  
Jehad Alzabut ◽  
Evren Hincal ◽  
Michal Niezabitowski
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Initial Conditions ◽  
Interval Matrix ◽  
Linear Matrix ◽  
Parameter Mismatch ◽  
Synchronization Problem ◽  
State Dependent

This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, the conventional robust control scheme cannot guarantee the synchronization of FOMBCNNs. Under the framework of the Filippov solution, the drive and response FOMBCNNs are first transformed into systems with interval parameters. Then, the new sufficient criteria are obtained by linear matrix inequalities (LMIs) to ensure the passivity in finite-time criteria for FOMBCNNs with mismatched switching jumps. Further, a feedback control law is designed to ensure the finite-time synchronization of FOMBCNNs. Finally, three numerical cases are given to illustrate the usefulness of our passivity and synchronization results.

Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties

2021 ◽  
Vol 420 ◽  
pp. 70-81
Author(s):  
Qiankun Song ◽  
Yanxi Chen ◽  
Zhenjiang Zhao ◽  
Yurong Liu ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Robust Stability ◽  
Parameter Uncertainties

scholarly journals Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohui Xu ◽  
Huanbin Xue ◽  
Yiqiang Peng ◽  
Jiye Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Delays ◽  
Average Dwell Time ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Switched Neural Networks ◽  
Globally Exponential Stability ◽  
Arbitrary Switching

In this paper, the stability of switched neural networks (SNNs) with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature.

scholarly journals Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Huanbin Xue ◽  
Yiqiang Peng ◽  
Quan Xu ◽  
Jibin Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
The Stability ◽  
Complex Valued

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example.

scholarly journals Robust Stability Analysis of Fractional-Order Hopfield Neural Networks with Parameter Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Shuo Zhang ◽  
Yongguang Yu ◽  
Wei Hu
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Robust Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Neural System ◽  
Hopfield Neural Networks ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Theoretical Results

The issue of robust stability for fractional-order Hopfield neural networks with parameter uncertainties is investigated in this paper. For such neural system, its existence, uniqueness, and global Mittag-Leffler stability of the equilibrium point are analyzed by employing suitable Lyapunov functionals. Based on the fractional-order Lyapunov direct method, the sufficient conditions are proposed for the robust stability of the studied networks. Moreover, robust synchronization and quasi-synchronization between the class of neural networks are discussed. Furthermore, some numerical examples are given to show the effectiveness of our obtained theoretical results.

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