Title: Mean-square asymptotic stability of stochastic inertial neural networks with time-delay and Markovian jump parameters

Authors: R. Krishnasamy; Raju K. George

Addresses: Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore – 641 004, Tamil Nadu, India ' Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram – 695 547, Kerala, India

Abstract: This paper investigates the stability of inertial neural networks (INNs) which incorporates the effects of both intrinsic and extrinsic noises along with time-delay. These intrinsic and extrinsic noises are taken to be in the form of Markovian jump parameters and Brownian motion respectively. Required sufficient stability conditions are established in the form of linear matrix inequalities from the construction of Lyapunov-Krasovskii functional. Derived conditions will be delay-dependent which includes information about the bounds of the time-delay and also its derivatives. Theory of Lyapunov stability, Ito calculus and linear matrix inequality are used to derive the main results. Numerical example is given to demonstrate the validity of the derived theoretical results.

Keywords: INNs; inertial neural networks; mean-square asymptotic stability; time-delay; Markovian jump; Lyapunov-Krasovskii functional.

DOI: 10.1504/IJDSDE.2021.120047

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.5/6, pp.527 - 541

Received: 13 Apr 2019
Accepted: 02 Nov 2019
Published online: 05 Jan 2022 *

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