Robust Stability Analysis Of Discrete-time Switched Hopfield Neural Networks

As an important class of hybrid dynamical system, the switched system can be usedto model many actual complex control system. Neural networks have beenextensively studied due to their successful applications in many areas. In recent years,however, discrete-time neural networks become more important than theircontinuous-time counterparts when implementing the neural networks in a digitalway.In this paper, we use the Lyapunov-Krasovskii functions, average dwell timeapproach and linear matrix inequality technology, this dissertation investigates therobust exponential stability problem for discrete-time switched Hopfield neuralnetworks with time-varying delay and uncertainty, construct the state feedbackcontrollers which satisfy the givenH_∞performance. Finally, several numericalexamples are given to illustrate the correctness of the proposed results. The mainwork and research results lie in the following.The first chapter is a brief introduction for the importance and the practical andtheoretical significance of the switched systems, and the research status of the neuralnetwork and switched Hopfield neural networks with time-varying delay. In thesecond chapter, some basic concepts of stability and basic control systems theory willbe introduced. The third chapter is concerned with the robust exponential stabilityproblem for discrete-time switched Hopfield neural networks with time-varying delayand uncertainty. Firstly, the mathematical model of the system is established. Then byconstructing a new Lyapunov-Krasovskii functional and using discrete-time Jensen’sinequality, linear matrix inequality (LMIs), average dwell time approach, a newdelay-dependent criteria is developed, which guarantee the robust exponentialstability of discrete-time switched Hopfield neural networks. A numerical example isprovided to demonstrate the effectiveness of the results obtained. The forth chapter isconcerned with the problem of robust stabilization andH_∞control for discrete-timeswitched Hopfield neural networks. By using the average dwell time approachtogether with the multiple Lyapunov function technique, we propose a state feedbackcontroller to guarantee that the switched Hopfield neural networks is robustlyexponentially stable with the disturbance attenuation level γ>0about its equilibrium point for all admissible uncertainties.