Global Exponential Stability For A Class Of Singular Time-Delay System And Analysis

The generalized systems, which are also called to be singular systems, are made of differential equations and algebra equation. it is widely appplied to the fields such as circuit analysis, economics, mechanics, chemics, biologics and so on. The generalized system is more complex than one described by ordinary differential equations. On the other hand, the phenomenon of time delays widespread exists in various systems. Therefore, it is an important subject to study singular system with time delays.In this paper, we investigate the global stability of the generalized system with finite delays and infinite delays, and analyze the stability of cobweb model. The main content is the followings.In the first part, we discuss the generalized systems with time delays. Firstly, we estiblish two singular differential inequalities with finite and infinite delays, respectely. Then, some sufficient conditions ensuring the global exponential stability of the zero is obtained for the singular delayed systems by using the inequalities and analysis skills.In the second part, we formulate a model of cobweb model described by singular systems with time delays. Then, the global stability of the model is given.