Stability of cellular neural networks with dominant nonlinear and delay-type templates

Roska, Tamás; Wu, Chai Wah; Chua, Leon O.

doi:10.1109/81.224300

Cited by 215 publications

(54 citation statements)

References 11 publications

(14 reference statements)

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“…References [1][2][3][4][5][6][7][8][9], and references therein. Indeed, such networks are ideally suited for solving optimization problems, since the property of global convergence prevents a network from the risk of getting stuck at some local minimum of the energy function to be minimized, and thus ensures that the global optimum is computed.…”

Section: Introductionmentioning

confidence: 99%

M‐matrices and global convergence of discontinuous neural networks

Forti

2006

Circuit Theory & Apps

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The paper considers a general class of neural networks possessing discontinuous neuron activations and neuron interconnection matrices belonging to the class of M-matrices or H-matrices. A number of results are established on global exponential convergence of the state and output solutions towards a unique equilibrium point. Moreover, by exploiting the presence of sliding modes, conditions are given under which convergence in finite time is guaranteed. In all cases, the exponential convergence rate, or the finite convergence time, can be quantitatively estimated on the basis of the parameters defining the neural network. As a by-product, it is proved that the considered neural networks, although they are described by a system of differential equations with discontinuous right-hand side, enjoy the property of uniqueness of the solution starting at a given initial condition. The results are proved by a generalized Lyapunov-like approach and by using tools from the theory of differential equations with discontinuous right-hand side. At the core of the approach is a basic lemma, which holds under the assumption of M-matrices or H-matrices, and enables to study the limiting behaviour of a suitably defined distance between any pair of solutions to the neural network

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Section: Introductionmentioning

confidence: 99%

M‐matrices and global convergence of discontinuous neural networks

Forti

2006

Circuit Theory & Apps

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“…Therefore, (2) is a more general CGNN. It includes several well known neural networks models as its special cases such as the Hopfield neural networks (see [1,2,11,15,16,21,29]), cellular neural networks (see [6,7,20]); etc.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability analysis of Cohen-Grossberg neural networks with time-varying delays

Yan

Huang

Yuan

2011

Acta Math. Appl. Sin. Engl. Ser.

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“…O primeiro, que não inclui qualquer informação sobre o tamanho do retardo no tempo, é conhecido como independente do retardo no tempo: Marcus and Westervelt (1989), Roska et al (1992), Roska et al (1993), Gopalsamy and He (1994a), Gopalsamy and He (1994b), Ye et al (1994), Zhang (1996), Liao and J.Yu (1998), den Driessche and Zou (1998), Liao and Yu (1998), Joy (1999), Joy (2000), Arik (2000), Cao (2000), Chen and Rong (2003) e Wang et al (2004). O outro conceito, leva em conta explicitamente o retardo no tempo na formulação do problema, sendo conhecido como dependente do retardo no tempo: Wei and Ruan (1999), Zhang et al (2003), Chen et al (2004), Li et al (2004), Ensari andArik (2005) e Zeng et al (2005).…”

Section: Introductionunclassified

Análise de estabilidade assintótica e exponencial em redes neurais artificiais sujeitas a retardo no tempo e a incertezas do tipo politópicas

Souza

Palhares

Ekel

2008

Sba Controle & Automação

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This paper presents sufficient conditions for asymptotic and exponential stability of a class of artificial neural networks (ANNs) subject to constant or time-varying delay and polytope-bounded uncertainties.The proposed approach is based on Lyapunov-Krasovskii stability theory, and the linear matrix inequalities (LMIs) technique introducing slack matrices so that convex optimization algorithms can be used.Three examples with numerical simulations are performed to demonstrate the effectiveness of the proposed method. The first example deals with the asymptotic stability analysis, the second one with the robust stability analysis and the last one with exponential stability. RESUMOEste artigo apresenta condições suficientes para estabilidade assintótica e exponencial de uma classe de RNAs (Redes Neurais Artificiais) sujeitas a influência de retardo no tempo (constante ou variante) e/ou sujeitas a incertezas paramétri-cas do tipo politópicas.A abordagem proposta é baseada na teoria de estabilidade de Lyapunov-Krasovskii, e utiliza desigualdades matriciais lineares (LMIs -do inglês, Linear Matrix Inequalities) introduzindo matrizes de relaxação, de modo que os resultados obtidos podem ser facilmente resolvidos por meio de algoritmos de otimização convexa.Três exemplos com simulações numéricas são usados para demonstrar a eficiência do método proposto. O primeiro exemplo analisa a estabilidade assintótica, o segundo a es-

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Stability of cellular neural networks with dominant nonlinear and delay-type templates

Abstract: We present some further stability results for cellular neural networks with nonlinear delay-type templates. In particular, we show that there exists a globally asymptotically stable equilibrium point in CNN's with dominant nonlinear delay-type templates.

Cited by 215 publications

References 11 publications

M‐matrices and global convergence of discontinuous neural networks

M‐matrices and global convergence of discontinuous neural networks

Exponential stability analysis of Cohen-Grossberg neural networks with time-varying delays

Análise de estabilidade assintótica e exponencial em redes neurais artificiais sujeitas a retardo no tempo e a incertezas do tipo politópicas

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