State estimator for neural networks with sampled data using discontinuous Lyapunov functional approach
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O R I G I N A L PA P E R
State estimator for neural networks with sampled data using discontinuous Lyapunov functional approach S. Lakshmanan · Ju H. Park · R. Rakkiyappan · H.Y. Jung
Received: 22 October 2012 / Accepted: 30 January 2013 / Published online: 12 February 2013 © Springer Science+Business Media Dordrecht 2013
Abstract In this paper, the sampled-data state estimation problem is investigated for neural networks with time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled data estimator is constructed. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. New delaydependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulations are given to demonstrate the usefulness and effectiveness of the presented results.
S. Lakshmanan · J.H. Park () · H.Y. Jung Nonlinear Dynamics Group, Department of Electrical Engineering/Information and Communication Engineering, Yeungnam University, 214-1 Dae-dong, Kyongsan 712-749, Republic of Korea e-mail: [email protected] S. Lakshmanan e-mail: [email protected] R. Rakkiyappan Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamilnadu, India
Keywords State estimator · Neural networks · Time-delays
1 Introduction In past two decades, there has been increasing research interests in analyzing the dynamic behaviors of neural networks due to their extensive applications such as signal processing, pattern recognition, engineering optimization, and associative memory [1–3]. These applications ensure the global exponential or asymptotic stability of designed neural networks. It is well believed that the inherent time delays may cause the oscillation and instability in many dynamical networks. On the other hand, as recommended by [4], the time delay is purposely introduced into the model of neural networks, which is more effective for some engineering applications such as speed detection of moving objects and processing of moving images. In general, the time delays can be usually categorized as constant delays, time-varying delays, and distributed delays. Therefore, the stability problems for delayed neural networks have been a growing research interest in recent years (for example, refer to [5–10]). Recently, the state estimation problem of delayed neural networks has motivated an enormous deal of interest, and considerable research efforts have been made on this fruitful topic (see, for example, [11– 25]). As is well known, a neural network is a highly
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interconnected network with a large number of neurons. In particular, a neural network is d
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