Stability Of Singular Systems With Time-Delay And Its Applications

Thesis based on the cobweb model in the economic system .By improving classical cobweb model, the cobweb model in a singular differential equation form with multi-products and Time-delay effects is established. For analysis the System equilibrium points exist and system stability of the equilibrium point, a generalized difference (differential) inequality with delays is established. Based on analyzing the existence of equilibrium point of the model, some sufficient conditions on the exponential stability of singular systems are obtained and the exponential convergence rate is estimated.The first part of article introduction the concept and theory of the development,research methods,research outlook of singular systems with time-delay. Research ideas and the main results of this article is also illustrate.The Part 2 of article introduction of knowledge of singular systems and the phylogeny of singular systems time-delay.The Part 3 of article introduction of the stability of singular discrete-time system with Time-delay, first of all introduction of the concept of this system's exponential stability. Next, a generalized difference inequality with delays is established. Based on the obtained inequality, we finally investigate the stability of the cobweb model.The Part 4 of article introduction the application of the systems in economic system. Use the obtained conclusions, we obtain the existence and exponential stability of equilibrium of cobweb model with multi-products and time delay effects.