State estimation of static neural networks with interval time-varying delays and sampled-data control
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State estimation of static neural networks with interval time-varying delays and sampled-data control M. Syed Ali1 · N. Gunasekaran1
Received: 28 September 2016 / Revised: 8 June 2017 / Accepted: 25 June 2017 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Abstract In this paper, we consider the problem of sampled-data control for static neural networks with interval time-varying delays. As opposed to the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. By converting the sampling period into a bounded time-varying delays, the error dynamics of the considered neural network is derived in terms of a dynamic system with two different time-delays. By constructing a suitable Lyapunov–Krasovskii functional with double and triple integral terms and using Jensen inequality, delay-dependent criteria are presented, so that the error system is asymptotically stable. Delay-dependent asymptotically stability condition is established in terms of linear matrix inequality (LMI) framework, which can be readily solved using the LMI toolbox. Finally, three examples are given to show the effectiveness of the theoretical results. Keywords Lyapunov method · Linear matrix inequality · Static neural networks · Sample-data control · Time-varying delay Mathematics Subject Classification 93CXX · 93DXX · 68TXX · 65KXX · 65LXX
1 Introduction In the past few decades, recurrent neural networks with time-varying delays have been associated viably in various domains, for instance, pattern recognition, associative memories, signal processing, parallel computation, optimization solvers, and so on. Time-delays rou-
Communicated by Jose Roberto Castilho Piqueira, Elbert E N Macau and Luiz de Siqueira Martins Filho.
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M. Syed Ali [email protected] N. Gunasekaran [email protected]
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Department of Mathematics, Thiruvalluvar University, Vellore 632 115, Tamilnadu, India
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M. S. Ali, N. Gunasekaran
tinely happen in sensible neural frameworks as a result of the restricted development paces of the amplifiers or the constrained sign inducing time in biological networks, which may actuate the undesirable component rehearses like influencing and instability. Along these lines, much thought has been paid to the examination of the stability analysis problem of neural frameworks with time-contrasting deferrals and a considerable measure of results have been available in Liu (2013), Syed Ali (2015), Feng et al. (2012), Wu and Wu (2009), and Lu et al. (2008). Neural networks can be ordered into two classes, that is, static neural networks and local field networks. In static neural networks, neuron states are picked as fundamental variables. While in local field systems, local field states are picked as essential variables. It has been demonstrated that these two sorts of neural networks are not generally proportionate (Xu et al. 2004). In contrasted and rich results for local field networks, results for static neural networks are substantial
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