Boundedness And Input To State Stability (ISS) Of Functional Differential Equations

In this paper, the boundedness, dissipativity and input to state stability (ISS) for functional differential equations are studied .In Chapter 1 , the development, background and research topics are outlined for functional differential systems. And the significance of this paper and main research work also are introduced.In Chapter 2, we mainly discussed the boundedness and the ultimate boundedness (uniform dissipativity) for functional differential equations. Firstly, the basic concept and fundamental theorems are introduced for functional differential equations. Then, the boundedness and dissipativity in ordinary differential equations are investigated. Lastly, we study the boundedness and dissipativity for functional differential equation.In Chapter 3, we first introduce the concept on input to sate stability(ISS) for functional differential equations. Then, we prove some basic theorems about input to stability for the time-delay systems and obtain the sufficient condition ensuring ISS for the time-delay system. Based on the obtained theorems, we investigate the ISS of Hopfield neural networks with time-delays.In Chapter 4, The main work in this article is summarized, and further research is pointed out for functional differential equations.