Reachable set bounding for a class of bidirectional associative memory NNSs with Markov jump switching parameters
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Reachable set bounding for a class of bidirectional associative memory NNSs with Markov jump switching parameters Zhang He1 · Junwei Lu2 · Yunliang Wei3 · Yuming Chu4
Received: 11 September 2017 / Revised: 29 November 2017 / Accepted: 18 December 2017 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018
Abstract This paper studies the problem how to estimate the reachable set for a class of delayed bidirectional associative memory neural network systems (NNSs), which have Markov switching parameters and unit-energy or unit-peak bounded disturbance inputs. The feature of the Markov jump bidirectional associative memory NNSs shows in the following twofold: the time delay is time varying; the transition rates is time varying. Moreover, the time-varying transition rates is piecewise constant. Using the Lyapunov functional method, delay-partitioning and linear matrix inequalities techniques, the estimate problem of the reachable set depending on time delay is solved. The effectiveness of the given results is illustrated by the proposed numerical examples. Keywords Markov jump · Reachable set estimation · Bidirectional associative memory NNSs · Piecewise-constant transition rates · Time delay
Communicated by Marcos Eduardo Valle.
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Zhang He [email protected] Junwei Lu [email protected] Yunliang Wei [email protected] Yuming Chu [email protected]
1
School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2
School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042, Jiangsu, China
3
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
4
School of Science, Huzhou Teachers College, Huzhou 313000, Zhejiang, China
123
Z. He et al.
Mathematics Subject Classification 00-01 · 99-00
1 Introduction Neural networks (NNs) widely existed in various fields of the real world and received a great deal of attention. Different kinds of neural networks models, such as recurrent NNs (Liu et al. 2006; Cao and Wang 2005), Hopfield NNs (Li et al. 2009), cellular NNs (He et al. 2006; Huang 2006), stochastic Cohen–Grossberg NNs (Zhang and Wang 2008), have been extensively investigated to deal with various issues in both theory and applications including pattern recognition, optimization, problem, face detection, motion control. Obviously, time delay inevitably occurs in real applications of neurons, especially at synaptic levels, due to the finite conduction speed of the amplifier or hardware implementations of NNs in the process of information transformation between two neurons. As a consequence, instability, sustained oscillations, bifurcation or chaos of NNs are resulted from time delays. NNs with time delay have been widely investigated and many results on this issue have been reported (He et al. 2007, 2014; Li and Liao 2005; Mou et al. 2008; Qi et al. 2015; Zhang et al. 2015; Zhang and Quan 2015; Cao and Wan 2014; Zeng et al. 2010; Huang et al. 2012, 2013; Li et al. 2011). Therein, Qi
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