Global exponential stability analysis for cellular neural networks with variable coefficients and delays

Kao, Yonggui; Gao, Cunchen

doi:10.1007/s00521-007-0121-y

Cited by 11 publications

(3 citation statements)

References 19 publications

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“…Cellular neural networks (CNNs) are large scale nonlinear circuits composed of locally connected cells, which was introduced in 1988 by Chua and Yang [1,2]. CNN has a tremendous variety of applications in the fields of dynamic systems and signal processing [3][4][5][6][7][8][9]. The analysis of the dynamic behavior for the class of CNNs without feedback interconnections from neighboring cells, namely the uncoupled CNNs, is one of the popular research topics.…”

Section: Introductionmentioning

confidence: 99%

Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

Lin

Hsieh

Jeng

2013

Mathematical Problems in Engineering

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If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

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Section: Introductionmentioning

confidence: 99%

Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

Lin

Hsieh

Jeng

2013

Mathematical Problems in Engineering

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“…Thus, the stability of equilibrium points is a prerequisite when CNNs are applied to problems of image processing, signal processing, or nonlinear algebraic equations. Many delay-independent and delay-dependent stability criteria for CNNs have been proposed over the past years, mainly based on Razumikhin techniques, the Lyapunov-Krasovskii functionals and linear matrix inequalities (LMIs) formulation [6][7][8][9][10][11]. However, the stability of many practical neural networks cannot always be guaranteed by these techniques.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Cost Stabilization of Time-varying Delay Cellular Neural Networks via Riccati Inequality Approach

2011

Neural Process Lett

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This letter deals with the guaranteed cost stabilization of time-varying delay cellular neural networks (DCNNs). Based on the Razumikhin theorem and via applying the zoned discussion and maximax synthesis method in DCNNs, the quadratic Riccati matrix inequality criterion for the guaranteed cost stabilization controller is designed to stabilize the given chaotic DCNNs. The minimization of the guaranteed cost of stabilization for the DCNNs is also given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost stabilization control and its corresponding minimization problem.

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“…Several synthesis procedures have been developed for designing symmetric and non‐symmetric neural network (Michel and Farrell, 1988; Liu and Michel, 1993; Park and Park, 2000). Besides synthesis methods, increased attention is also being paid lately on the issue of stability in the dynamic behavior of these systems in the presence of time delays (Arik and Tavsanoglu, 2005; Park, 2006, 2008; Kao and Gao, 2008; Zeng et al , 2008), typically addressed in the context of Lyapunov‐Krasovksii functionals, and linear matrix inequalities (LMIs) formulated based on bounds related to these delays. This particular research direction, however, falls outside the scope of this paper, since the patterns we are interested in identifying are static.…”

Section: Introductionmentioning

confidence: 99%

Spatially distributed cellular neural networks

Bhambhani

Valbuena‐Reyes

Tanner

2011

International Journal of Intelligent Computing and Cybernetics

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Purpose-The objective of this work is to develop a methodology for the design of cellular neural networks with interconnection topologies optimized and suitable for spatially distributed implementation. Design/Methodology/Approach-We perform combinatorial optimization on the neural network's topology to obtain a sparser network, in which the links between the components of the network that reside in different physical locations are minimized. The approach builds on existing computationally efficient tools for the design of cellular neural networks and uses the concept of the network's stability parameters to assess the performance of the network prior to testing. Findings-It turns out that the sparser cellular neural networks thus produced exhibit performance that can be on par with that of networks with full connectivity, and that for implementations of modest size, communication delays are not that significant to affect the stability of the dynamical system. Originality/Value-The novelty of the proposed approach lies in the formulation of the combinatorial optimization problem in a way that trades-off network performance for communication overhead, and the use of this method for the physical implementation of associative memories across different interconnected processors.

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Global exponential stability analysis for cellular neural networks with variable coefficients and delays

Cited by 11 publications

References 19 publications

Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

Guaranteed Cost Stabilization of Time-varying Delay Cellular Neural Networks via Riccati Inequality Approach

Spatially distributed cellular neural networks

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