Passivity Analysis For Several Classes Of Neural Networks With Time-Varying Delays

As a typical nonlinear dynamical system, neural networks hold complex dynamic characteristics. They have been successfully applied to various fields, such as pattern recognition, associative memory, signal processing, fixed point computation and other scientific areas. However, in the process of neural networks circuit’s implementation, time delays present inevitably due to the influence of signal transmission and the finite switching speeds of the amplifiers. As is well known, time delays in neural networks is a source of oscillation, instability and other poor performances. For passivity being a higher level of stability, researching the passivity of neural networks with time delays has great theoretical and practical significance.This paper firstly introduces the development process of neural networks and passivity theory, the background importance of the research subject. And the current research status of passivity about time-delayed neural networks is discussed. Then, we have analyzed the passivity about Hopfield neural networks model with time-varying delay, neural networks model with time-varying interval delay in both the system state and output and neutral-type neural networks with mixed delays. According to the Lyapunov stability theorem, we utilize some techniques synthetically, such as Refined Jensen-based inequality, reciprocally convex combination, free-weighting matrix and Schur complements lemma, to estimate some important integral items of Lyapunov functional’s derivative. And some less conservative passivity conditions are obtained. Finally, we verify the feasibility of the conclusions through the LMI toolbox in MATLAB.The main works are described as follows:(1) By utilizing the Schur complements lemma, Jensen inequality and Lyapunov stability theorem, we have studied the passivity analysis of variable time-delay Hopfield neural networks and parameter uncertain time-delay Hopfield neural networks. Corresponding to the two models, the sufficient conditions of the passivity are obtained. We prove the feasibility of the conclusions through the LMI toolbox in MATLAB.(2) Based on the Refined Jensen-based inequality, reciprocally convex combination and proper Lyapunov functional, we have researched the passivity analysis of neural networks with time-varying interval delay in both the system state and output, and a sufficient conditions is presented. Less conservative passivity condition can be gained. The validity of the conclusion is proved by a numerical comparison.(3) We study the passivity problem of neutral-type neural networks with mixed delays by using Free-Matrix-Based integral inequality, reciprocally convex combination and Lyapunov stability theorem. An numerical example is provided to demonstrate the feasibility of result.