Integral Type Halanay Inequality And Its Application In Stochastic Time-Delay Systems

The Halanay inequality,proposed by Halanay in 1966,is a powerful tool for analyzing stability of delayed differential systems.In recent years,the Halanay inequality has been widely applied and has many versions,including vector form,pulse form,fractional form,and unbounded delayed form.It has played a key role in many fields,such as the design and application of neural networks,synchronization of coupled oscillators,consensus problems in networked control systems and secure communication systems.This paper extends the differential Halanay inequality to the integral Halanay inequality and discusses the stability of neutral-type stochastic delayed systems and non-autonomous stochastic delayed reaction-diffusion neural networks,respectively.In Chapter 1,the research background,significance,main research questions,and innovative points of this thesis are first introduced.Then,some basic concepts and theoretical knowledge of stochastic systems involved in this paper are presented.In Chapter 2,the neutral-type stochastic delay system with both L evy noise and Markovian switching is described,and the concepts of input state stability,practical exponential stability,and pth moment exponential stability are given.Using the integral-type Halanay inequality,the moment exponential stability of the input state of the neutral-type stochastic delay system with L evy noise is proved.In Chapter 3,the non-autonomous stochastic delayed reaction-diffusion neural network with Markovian switching is described,and the concepts of stability and asymptotic stability are presented.Using the integral Halanay inequality,the moment stability,moment asymptotic stability,and moment exponential stability of this network are analyzed.In Chapter 4,the main research conclusions of this paper are presented and the prospects for future research are discussed.