Quasi-Synchronization of Time Delay Markovian Jump Neural Networks With Impulsive-Driven Transmission and Fading Channels

The problem of quasi-synchronization (QS) for the Markovian jump master-slave neural networks with time-varying delay is studied in this article, where the mismatch parameters and unreliable communication channels are considered as well. A set of stochastic variables with different expectations are used to describe the fading phenomena of parallel communication channels. An impulsive-driven transmission strategy is designed to reduce the communication load, and a corresponding impulsive controller is then designed. A synchronization error system (SES) is obtained, and a convex QS condition is established for the SES. A linear matrix inequality-based iterative algorithm is proposed to reduce the bound of the SES, and the corresponding controller gains are calculated. A numerical example is provided to illustrate the effectiveness of the developed result.

I. Introduction

Master–slave (MS) systems widely exist in the control field, where the slave system aims to follow the trajectory of the master system [1], [2]. Due to the advantages of the MS systems, they have been applied in many areas, for instance, maxillary sinus surgery [3], multiautonomous underwater vehicle cooperative navigation [4], teleoperation [5], and so on. In the past several decades, some important methods have been proposed to deal with different kinds of MS systems. In [6], the T–S fuzzy approach was used to handle nonlinear MS systems with time delays, and the system stable condition was established on the basis of the linear matrix inequality (LMI) approach. In [7], the sliding model method was employed to design the nonlinear filter to stabilize the force projecting the MS systems. What we have to point out is that neural networks (NNs) can be used to deal with nonlinear systems effectively [8]–[11], especially, with the development of the deep learning [12], [13]. Researchers have paid attention to the MS systems modeled by NNs, such as synchronization of chaotic [14], coordinated mobile manipulators [15], etc. It is worth further studying the NNs-based MS systems.