Journal ArticleDOI
LMI Conditions for Global Stability of Fractional-Order Neural Networks
TLDR
Some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems are proposed and a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition.Abstract:
Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.read more
Citations
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Journal ArticleDOI
Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay
TL;DR: Some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality and the obtained LMI results provide new insights into the research of delayed fractiona-order nonlinear systems.
Journal ArticleDOI
Adaptive control for fractional order induced chaotic fuzzy cellular neural networks and its application to image encryption
TL;DR: An image encryption algorithm is proposed by considering the FOFCNN as pseudo-random number generator (PRNG), which outperforms the existing encryption algorithms and ensures the global asymptotic and exponential stability are derived in a novel manner.
Journal ArticleDOI
Adaptive Fractional Fuzzy Integral Sliding Mode Control for PMSM Model
TL;DR: This paper addresses the stabilization problem of permanent magnet synchronous motor (PMSM) based wind energy conversion system (WECS) through a novel adaptive fractional fuzzy integral sliding mode control scheme in contrast to the traditional integer order control schemes.
Journal ArticleDOI
Global Nonfragile Synchronization in Finite Time for Fractional-Order Discontinuous Neural Networks With Nonlinear Growth Activations
Xiao Peng,Huaiqin Wu,Jinde Cao +2 more
TL;DR: Under the fractional Filippov differential inclusion framework, by utilizing the Lur’e Postnikov-type Lyapunov functional, nonsmooth analysis method, and the convergence properties developed in this paper, the synchronization conditions are derived in the form of linear matrix inequalities.
Journal ArticleDOI
Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks
Grienggrai Rajchakit,Pharunyou Chanthorn,Michal Niezabitowski,Ramachandran Raja,Dumitru Baleanu,A. Pratap +5 more
TL;DR: Analysis of a class of memristor-based fractional-order competitive neural networks by using Caputo’s fractional derivation finds that some sufficient conditions are obtained by linear matrix inequalities (LMIs) to ensure the stability and passivity of the MBFOCNNs, which can be effectively solved by the LMI computational tool in MATLAB.
References
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Book
Theory and Applications of Fractional Differential Equations
TL;DR: In this article, the authors present a method for solving Fractional Differential Equations (DFE) using Integral Transform Methods for Explicit Solutions to FractionAL Differentially Equations.
Journal ArticleDOI
Neurons with graded response have collective computational properties like those of two-state neurons.
TL;DR: A model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied and collective properties in very close correspondence with the earlier stochastic model based on McCulloch - Pitts neurons are studied.
Book
Neurons with graded response have collective computational properties like those of two-state neurons
TL;DR: In this article, a model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied, which has collective properties in very close correspondence with the earlier stochastic model based on McCulloch--Pitts neurons.
Journal ArticleDOI
Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
TL;DR: It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the LyAPunov functional approach, will ultimately handle all of the physically important cases.