Robust dissipativity and passivity of stochastic Markovian switching CVNNs with partly unknown transition rates and probabilistic time-varying delay

Qiang Li; Weiqiang Gong; Linzhong Zhang; Kai Wang; Qiang Li; Weiqiang Gong; Linzhong Zhang; Kai Wang

doi:10.3934/math.20221068

AIMS Mathematics

2022, Volume 7, Issue 10: 19458-19480. doi: 10.3934/math.20221068

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Research article

Robust dissipativity and passivity of stochastic Markovian switching CVNNs with partly unknown transition rates and probabilistic time-varying delay

1.
School of Science, Anhui Agricultural University, Hefei 230036, China
2.
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China

Received: 19 July 2022 Revised: 22 August 2022 Accepted: 24 August 2022 Published: 02 September 2022
MSC : 00A69

This article addresses the robust dissipativity and passivity problems for a class of Markovian switching complex-valued neural networks with probabilistic time-varying delay and parameter uncertainties. The main objective of this article is to study the proposed problem from a new perspective, in which the relevant transition rate information is partially unknown and the considered delay is characterized by a series of random variables obeying bernoulli distribution. Moreover, the involved parameter uncertainties are considered to be mode-dependent and norm-bounded. Utilizing the generalized It$ \hat{o} $'s formula under the complex version, the stochastic analysis techniques and the robust analysis approach, the $ (M, N, W) $-dissipativity and passivity are ensured by means of complex matrix inequalities, which are mode-delay-dependent. Finally, two simulation examples are provided to verify the effectiveness of the proposed results.
- complex-valued neural networks,
- dissipativity,
- Markovian switching,
- partly unknown transition rates,
- probabilistic time-varying delay
Citation: Qiang Li, Weiqiang Gong, Linzhong Zhang, Kai Wang. Robust dissipativity and passivity of stochastic Markovian switching CVNNs with partly unknown transition rates and probabilistic time-varying delay[J]. AIMS Mathematics, 2022, 7(10): 19458-19480. doi: 10.3934/math.20221068

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Abstract

This article addresses the robust dissipativity and passivity problems for a class of Markovian switching complex-valued neural networks with probabilistic time-varying delay and parameter uncertainties. The main objective of this article is to study the proposed problem from a new perspective, in which the relevant transition rate information is partially unknown and the considered delay is characterized by a series of random variables obeying bernoulli distribution. Moreover, the involved parameter uncertainties are considered to be mode-dependent and norm-bounded. Utilizing the generalized It$ \hat{o} $'s formula under the complex version, the stochastic analysis techniques and the robust analysis approach, the $ (M, N, W) $-dissipativity and passivity are ensured by means of complex matrix inequalities, which are mode-delay-dependent. Finally, two simulation examples are provided to verify the effectiveness of the proposed results.

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