Journal ArticleDOI
Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays
TLDR
New delay-dependent sufficient conditions ensuring global exponential stability for the system presented here are related to the size of the proportional delay factor, by employing matrix theory and Lyapunov functional, and without assuming the differentiability, boundedness and monotonicity of the activation functions.Abstract:
Global exponential stability of a class of cellular neural networks with multi-proportional delays is investigated. New delay-dependent sufficient conditions ensuring global exponential stability for the system presented here are related to the size of the proportional delay factor, by employing matrix theory and Lyapunov functional, and without assuming the differentiability, boundedness and monotonicity of the activation functions. Two examples and their simulation results are given to illustrate the effectiveness of the obtained results.read more
Citations
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Journal ArticleDOI
Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication
TL;DR: This paper is concerned with the finite-time and the fixed-time synchronization problem for a class of inertial neural networks with multi-proportional delays and some new and effective criteria are established to achieve finite- time and fixed- time synchronization of the master/slave of addressed systems.
Journal ArticleDOI
Periodicity of non-autonomous inertial neural networks involving proportional delays and non-reduced order method
Chuangxia Huang,Hua Zhang +1 more
TL;DR: By combining Lyapunov function method with differential inequality approach, non-reduced order method is used to establish some novel assertions on the existence and generalized exponential stability of periodic solutions for the addressed model.
Journal ArticleDOI
Global asymptotic stability of cellular neural networks with proportional delays
TL;DR: By using matrix theory and constructing suitable Lyapunov functional, delay-dependent and delay-independent sufficient conditions are obtained for the global asymptotic stability of cellular neural networks with proportional delays.
Journal ArticleDOI
Finite-time stability of a class of non-autonomous neural networks with heterogeneous proportional delays
Le Van Hien,Doan Thai Son +1 more
TL;DR: By introducing a novel constructive approach, new explicit conditions in terms of matrix inequalities ensuring that the state trajectories of the system do not exceed a certain threshold over a pre-specified finite time interval are derived.
Journal ArticleDOI
Asymptotic stability of cellular neural networks with multiple proportional delays
TL;DR: Sufficient conditions for delay-dependent global asymptotic stability and delay-independent uniform asymPTotic stability of the system are obtained by employing matrix theory and constructing Lyapunov functional.
References
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Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Book
The stability of dynamical systems
TL;DR: In this paper, an introduction to aspects of the theory of dynamical systems based on extensions of Liapunov's direct method is presented and the main ideas and structure for the theory are presented for difference equations and for the analogous theory for ordinary differential equations and retarded functional differential equations.
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Cellular neural networks with non-linear and delay-type template elements and non-uniform grids
Tamás Roska,Leon O. Chua +1 more
TL;DR: This paper extends the current repertoire of CNN cloning template elements (atoms) by introducing additional non-linear and delay-type characteristics and shows that the CNN with these generalized cloning templates has a general programmable circuit structure (a prototype machine) with analogue macros and algorithms.
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