Stability Analysis For The MIMO Nonlinear System Which Has Singular Perturbation

In 2003, Professor D.Angli and Professor Eduardo D.Sontag published an academic article which named Monotone control system in IEEE Transactions on Automatic control. This article laid the theoretical foundation for the development of the monotone control system. The monotone control system is one of hot research subjects in the control system, and plays an important role in the research of Biological control system. The theory which about monotone control system provides a new method about the studying of the stability for one system. At present, the theory is mainly applied into the Biological system, but a lot of real systems are nomonotone, so we can use the method which putted forward by the professor E.D.Sontag to decompose the nonmonotone system into the monotone system. This method provides the technical foundation for the studying about the stability of the system. The paper is organized as this follows:In the first chapter, the born and development of the monotone dynamics system as well as the background and development of the monotone control system. A brief introduce about the development of nonlinear system and singular perturbation.In the second chapter, we introduce the definition of monotone control system and the criterion about the stability of monotone control system.In the third chapter, we decompose the nonmonotone control system into a interconnection monotone system by the symmetric system. And discuss the global stability about interconnection system which has the negative feedback.In the fourth chapter, based on the perturbed theory and control theory, discuss the system which has a small perturbationε, and the asymptotic stability for it.In the fifth chapter, some concluding remarks are gibed and further works are point out.