The Condition And Method Of Stability Criterion Of Singular Large-scale Systems

Since Rosenbrok.H.H. first presented the problem of singular system in his research paper in 1974, singular systems has been aroused great interest of many people all over the world, and it has become a branch of modem control theory. With the rapid development of modem technology science and the need of large engineering technology, in order to overcome the difficulty what come from the increasing dimension of its mathematical model, people have proposed the singular large-scale system. The research of large scale systems has aroused great interest of the control and mathematical circles and has become one of the hot spot subjects. The stability of singular large scale systems is as important as that of the normal large scale systems. Because the singular systems are concerned with not only stability but also their regularity and impulse-free behaviors, the research of stability of singular large scale systems are much more complicated than those of regular systems.In this dissertation, a detailed analysis of the current situation of study on the stability of singular large-scale systems is studied and the stability of singular large-scale systems is scientific researched. The main results in this dissertation are as follows:1. The background related to the subject is summarized, and the Comparison principle and the method of Lyapunov function are introduced.2. The asymptotic stability and instability of a kind of continuous singular large-scale systems is investigated, respectively, by using the method of vector Lyapunov function under the condition that all isolated subsystems are asymptotically stable or unstable. The asymptotic stability and instability theorems are obtained, and the interconnecting parameter regions of stability and instability are also given. Some illustrate examples are given to show the results are pithy and easy to apply.3. The asymptotic stability and instability of a kind of discrete singular large scale systems is investigated by using the method of weight sum type Lyapunov function under the condition that all isolated subsystems are regular and asymptotically stable or unstable. The asymptotic stability theorem instability theorems are obtained, and the interconnecting parameter regions of stability and instability are also given. The interconnecting parameter regions of stability can be optimized.