Improved Stabilization Results for Markovian Switching CVNNs with Partly Unknown Transition Rates
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Improved Stabilization Results for Markovian Switching CVNNs with Partly Unknown Transition Rates Qiang Li1 · Jinling Liang1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, stochastic stability and stabilization problems are investigated for the Markovian switching complex-valued neural networks with mixed delays, where the transition rates (TRs) of the Markov chain are partly unknown, which might reflect more the realistic dynamical behaviors of the neural networks. On the basis of the Lyapunov stability theory and the stochastic analysis method as well as the properties of the TR matrix, several mode-dependent criteria are derived to guarantee the considered complex-valued network to be globally asymptotically stable in mean-square sense. Then, by proposing an appropriate mode-dependent controller, stabilization conditions in terms of matrix inequalities are derived to guarantee the closed-loop system to be stochastically mean-square stable. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical results. Keywords Complex-valued neural networks · Markovian switching · Partly unknown transition rates · Stochastic stability · Stabilization
1 Introduction In the past decades, research on of the dynamical neural networks has drawn plenty of attentions from researchers in different research fields, mainly due to their promising and widespread applications in pattern recognition, engineering optimization, signal processing, associative memory, filtering, antenna design, speech synthesis, computer vision, remote sensing and sonic waves, see Refs. [1–5] and the references cited therein for example. It is well known that complex-valued neural networks (CVNNs) have a prodigious superiority when dealing with some special problems. It has been revealed that CVNNs can not only characterize the more complicated physical properties of the original system, but also solve many problems which cannot be solved with the real-valued ones, such as the XOR problem and the detection of symmetry problem [6,7]. In addition, other novel applications concerning CVNNs are also found in meta-cognitive learning framework (MCLF) and wind profile
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Jinling Liang [email protected] School of Mathematics, Southeast University, Nanjing 210096, China
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Q. Li, J. Liang
model (WPM). For example, in [8], a meta-cognitive learning framework has been presented to control the learning process of a fully complex-valued radial basis function, where major advantages are reported over the existing approaches, as specially its classification abilities in MCLF. Speed and direction of the wind signals have been tackled as an entire complex vector in [9] to construct a well-performed WPM by fulling utilizing the properties of the CVNNs. All of them verify the necessity/urgency to further tackle the CVNNs, and numerous revelent achievements have been reported in the literature [10–15]. As is known to all, time delay is entrenched and ubiquitous in the pro
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