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1. An overview of recent developments in Lyapunov–Krasovskii functionals and stability criteria for recurrent neural networks with time-varying delays.

Author

Zhang, Xian-Ming, Han, Qing-Long, Ge, Xiaohua, and Ding, Derui

Subjects
*LYAPUNOV functions, *ARTIFICIAL neural networks, *LYAPUNOV stability, *NEURONS, *NONLINEAR functions
Abstract

Global asymptotic stability is an important issue for wide applications of recurrent neural networks with time-varying delays. The Lyapunov–Krasovskii functional method is a powerful tool to check the global asymptotic stability of a delayed recurrent neural network. When the Lyapunov–Krasovskii functional method is employed, three steps are necessary in order to derive a global asymptotic stability criterion: (i) constructing a Lyapunov–Krasovskii functional, (ii) estimating the derivative of the Lyapunov–Krasovskii functional, and (iii) formulating a global asymptotic stability criterion. This paper provides an overview of recent developments in each step with insightful understanding. In the first step, some existing Lyapunov–Krasovskii functionals for stability of delayed recurrent neural networks are anatomized. In the second step, a free-weighting matrix approach, an integral inequality approach and its recent developments, reciprocally convex inequalities and S -procedure are analyzed in detail. In the third step, linear convex and quadratic convex approaches, together with the refinement of allowable delay sets are reviewed. Finally, some challenging issues are presented to guide the future research. [ABSTRACT FROM AUTHOR]

Published
2018
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2. Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects.

Author

Chen, Jiyang, Li, Chuandong, and Yang, Xujun

Subjects
*ARTIFICIAL neural networks, *ENGINEERING, *LYAPUNOV functions, *STABILITY theory, *NEURONS
Abstract

Abstract In this paper, we investigate the asymptotic stability of fractional-order fuzzy neural networks with fixed-time impulse and time delay. According to the fractional Barbalat's lemma, Riemann–Liouville operator and Lyapunov stability theorem, some sufficient conditions are obtained to ensure the asymptotic stability of the fractional-order fuzzy neural networks. Two numerical examples are also given to illustrate the feasibility and effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Published
2018
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3. Design of state estimator for BAM fuzzy cellular neural networks with leakage and unbounded distributed delays.

Author

Ratnavelu, K., Manikandan, M., and Balasubramaniam, P.

Subjects
*NEURAL circuitry, *ASSOCIATIVE memory (Psychology), *NEURONS, *LINEAR matrix inequalities, *LYAPUNOV functions
Abstract

In this paper, the state estimation problem is studied for the bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with delays, where the delays include leakage and unbounded distributed delays. The problem addressed is to estimate the neuron states, through available output measurements, such that for all admissible leakage and unbounded distributed delays, the dynamics of the estimation error is globally asymptotically stable. A delay-dependent linear matrix inequality (LMI) criterion for the existence of the estimator is proposed by using the Lyapunov–Krasovskii functional method. In addition, the unknown gain matrix is determined by solving a delay-dependent LMI. Finally, numerical examples and simulations are provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Published
2017
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