Impulsive Control And Synchronization Of Complex-valued Neural Networks Based On LMI Technology

With the development of science and technology,real-valued neural networks are no longer sufficient to study many problems in the fields of biology and engi-neering.The complex-valued neural network is more superior in signal processing and other aspects,having gradually received the attention of scholars worldwide In addition,impulsive control,as a discontinuous control method,can effectively reduce the control cost and is easy to implement.It provides a powerful tool for the stability and synchronization of complex-valued neural networksThis paper mainly studies the impulsive control and synchronization of delayed complex-valued neural networks.It mainly includes the followingIn Chapter 1,we introduce the research background and research status of complex-valued neural networks and impulsive control,and specifies the basic structure and the required definitions and lemmas of this paper.In Chapter 2,we mainly study the impulsive control problem of delayed complex-valued neural network,which fully considers the influence of discrete time delay,distributed time delay and uncertain parameters on the system.By designing a delayed impulsive controller,applying the Lyapunov method,impulsive differential inequality,and linear matrix inequalities(LMIs)techniques,the sufficient condition for ensuring the global exponential stability of delayed complex-valued neural networks is given.Finally,an example with numerical simulation is used to verify the feasibility of the conclusions.In Chapter 3,we mainly study the synchronization of complex-valued interval neural networks with mixed delays under the control of distributed delayed impulsive control.By constructing complex-valued Lyapunov functions and adopting drive-response synchronization method and using the delayed impul-sive differential inequality technique,an exponential Lag synchronization criterion and controller design method that depend on discrete and distributed delays are established.The obtained criteria are expressed by complex-valued LMIs and are easy to implement with the toolbox in Matlab.Finally,numerical simulations are performed through examples to verify the validity of the conclusions as well.