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On Complex Artificial Higher Order Neural Networks: Dealing with Stochasticity, Jumps and Delays

On Complex Artificial Higher Order Neural Networks: Dealing with Stochasticity, Jumps and Delays
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Author(s): Zidong Wang (Brunel University, UK), Yurong Liu (Yangzhou University, China) and Xiaohui Liu (Brunel University, UK)
Copyright: 2009
Pages: 378
Source title: Artificial Higher Order Neural Networks for Economics and Business
Source Author(s)/Editor(s): Ming Zhang (Christopher Newport University, USA)
DOI: 10.4018/978-1-59904-897-0.ch021

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Abstract

This chapter deals with the analysis problem of the global exponential stability for a general class of stochastic artificial higher order neural networks with multiple mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this chapter is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both the mixed time delays and Markovian switching. By employing a new Lyapunov-Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria ensuring the exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.

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