Stability Analysis of Markov Jump Neural Networks With Mixed Delays in Finite Frequency Domain Based on PDC Controller

Nuo Xu,Liankun Sun

doi:10.1109/access.2019.2941976

Nuo Xu, Liankun Sun

Open Access

https://doi.org/10.1109/access.2019.2941976

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Journal: IEEE Access	Publication Date: Jan 1, 2019
Citations: 1	License type: CC BY 4.0

Affiliation: Tianjin Polytechnic University

Abstract

In this paper, the stability of Markov jumping neural network (MJNN) with mixed delays under the control of finite frequency domain Parallel Distributed Compensation (PDC) controller is studied. By introducing the generalized-KYP lemma, the frequency domain analysis is combined with the neural network. The positive definite and negative definite conditions in Lyapunov stability theory are improved by using Bessel-Legendre inequality method. Sufficient conditions for the stability of the system are given and proved. Finally, numerical examples show that the system can maintain stability under the control of the PDC controller at low, medium and high frequencies.

Highlights

In the past decades, due to the wide application of neural network in signal processing, pattern recognition, static image processing, associative memory and many other fields, considerable attention has been paid to the stability of neural network, and abundant research results have been achieved [1]–[4]
This paper will make correlation stability analysis based on Markov jump neural network system (MJNN)
Based on Lyapunov stability theory and linear matrix inequality (LMI) method, a lot of research results have been achieved in various kinds of neural networks, such

Summary

INTRODUCTION

Due to the wide application of neural network in signal processing, pattern recognition, static image processing, associative memory and many other fields, considerable attention has been paid to the stability of neural network, and abundant research results have been achieved [1]–[4]. Based on Lyapunov stability theory and linear matrix inequality (LMI) method, a lot of research results have been achieved in various kinds of neural networks, such. Sun: Stability Analysis of MJNN With Mixed Delays in Finite Frequency Domain Based on PDC Controller as neutral, impulsive, stable with mixed delay and Markov jump. In order to satisfy condition two, scholars have proposed many useful inequality methods, such as Jensen inequality [14], Wirtinger inequality [15], Free matrix inequality [16], improved Wirtinger inequality [17] and so on. The third problem studied in this paper is to reduce the conservativeness of positive and negative definite conditions of Lyapunov functional by using the Bessel-Legendre inequality method.

PROBLEM FORMULATION

DESIGN OF PDC CONTROLLER IN FINITE

AN IMPROVED POSITIVE DEFINITE RULE

NUMERICAL EXAMPLES

CONCLUSION