Passivity analysis for Markovian jumping neutral type neural networks with leakage and mode-dependent delay

Natarajan Mala; Arumugam Vinodkumar; Jehad Alzabut; Natarajan Mala; Arumugam Vinodkumar; Jehad Alzabut

doi:10.3934/biophy.2023012

AIMS Biophysics

2023, Volume 10, Issue 2: 184-204. doi: 10.3934/biophy.2023012

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Passivity analysis for Markovian jumping neutral type neural networks with leakage and mode-dependent delay

1.
Department of Mathematics, Kovai Kalaimagal College of Arts and Science, Coimbatore-641 109, Tamil Nadu, India
2.
Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India
3.
Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
4.
Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey

Received: 09 January 2023 Revised: 05 April 2023 Accepted: 16 April 2023 Published: 28 April 2023

In this study, we discuss the passivity analysis for Markovian jumping Neural Networks of neural-type. The results are demonstrated using phases of linear matrix inequalities as well as an improved Lyapunov-Krasovskii functional (LKF) of the triple integral terms and quadruple integrals. The information of the mode-dependent of all delays have been taken into account in the constructed Lyapunov–Krasovskii functional and novel stability criterion is derived. The value of selecting as many Lyapunov matrices that are mode-dependent as possible is demonstrated. The effectiveness and decreased conservatism of the aforementioned theoretical results are eventually demonstrated by a numerical example.
- Markov jump neural networks,
- Lyapunov-Krasovskii functional,
- Linear matrix inequality,
- Passivity theory
Citation: Natarajan Mala, Arumugam Vinodkumar, Jehad Alzabut. Passivity analysis for Markovian jumping neutral type neural networks with leakage and mode-dependent delay[J]. AIMS Biophysics, 2023, 10(2): 184-204. doi: 10.3934/biophy.2023012

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Abstract

In this study, we discuss the passivity analysis for Markovian jumping Neural Networks of neural-type. The results are demonstrated using phases of linear matrix inequalities as well as an improved Lyapunov-Krasovskii functional (LKF) of the triple integral terms and quadruple integrals. The information of the mode-dependent of all delays have been taken into account in the constructed Lyapunov–Krasovskii functional and novel stability criterion is derived. The value of selecting as many Lyapunov matrices that are mode-dependent as possible is demonstrated. The effectiveness and decreased conservatism of the aforementioned theoretical results are eventually demonstrated by a numerical example.

Acknowledgments

J. Alzabut is thankful to Prince Sultan University and OSTİM Technical University for their endless support during the achievement of this paper.

Conflicts of interest

Availability of data and materials: Not applicable. On behalf of all authors, the corresponding author declares that they have no conflict of interest.

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