Abstract
This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.
Highlights
Due to the great significance of neural networks (NNs) for both practical and theoretical purposes, their dynamics have been explored widely in recent years, such as pattern recognition, signal processing, solving optimization problems, static image processing, associative memories, target tracking, and automatic control. erefore, many research subjects have been studied in a broad spectrum of stability analysis, passivity analysis, control, filtering design, and state estimation and synchronization, concerning to NNs [1,2,3,4,5,6]
In an Markovian jump neural networks (MJNNs), hopping among operation modes is specified by a Markov process, so it is Mathematical Problems in Engineering important to understand the impacts of its stochastic attributes on the stability analysis of delayed MJNNs
Given an initial bounded state, we require the system to remain in a state that is not superior to a particular threshold during a specified time interval. Since this type of stability ensures a faster convergence of the system, it has been widely used in various NNs, such as the MJNNs, and synchronizing neural networks [24]
Summary
Due to the great significance of neural networks (NNs) for both practical and theoretical purposes, their dynamics have been explored widely in recent years, such as pattern recognition, signal processing, solving optimization problems, static image processing, associative memories, target tracking, and automatic control. erefore, many research subjects have been studied in a broad spectrum of stability analysis, passivity analysis, control, filtering design, and state estimation and synchronization, concerning to NNs [1,2,3,4,5,6]. In [20], the authors conducted an asymptotic stability analysis for stochastic and static NNs with time-varying delays that are mode-dependent. E mode-dependent MJNNs with time-varying delays and incomplete transition rates can be found in [23], wherein some LMI-based conditions are proposed to obtain the required results. Given an initial bounded state, we require the system to remain in a state that is not superior to a particular threshold during a specified time interval Since this type of stability ensures a faster convergence of the system, it has been widely used in various NNs, such as the MJNNs, and synchronizing neural networks [24]. Notations are as follows: Rn: n-dimensional Euclidean space P > 0: the matrix P is a symmetric matrix min (P): minimum eigenvalue of P max(P): maximum eigenvalue of P I: identity matrix diag {·}: diagonal matrix ∗ : symmetric matrices
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