一种新的线性时变系统区间稳定性判别方法

A New Method to Evaluate the Stability of Linear Time Varying System

线性时变系统在自动控制的理论和应用方面都有重要的意义。对这类系统,目前已有多种方法对其进行研究。其中利用时变系统区间矩阵的上下界的性质来判断其稳定性的方法,即所谓的M矩阵法是重要的方法之一。利用矩阵相似变换和向量比较原理研究了线性时变系统区间稳定性问题,在M矩阵法的基础上,提出了新的判别方法,扩大了原有方法的应用范围,使稳定区域的保守性进一步降低。特别是对某些原来M矩阵法无法分析的系统,提出了更具有应用价值的方法,并给出示例,验证了该方法的正确性。

Linear time - varying system plays important role in control theory both in theoretical and practical aspects. Many methods have been developed to analyze this system. Among those methods, the method to analyze the stability of the system by the up- down boundary of the system's matrix, so called M - method, is one of the main tools in analyzing this kind of system. Based upon the previous M - method, with the help of the similar transformation and vector- comparison theorem, a new method is set up to analyze this system. Expanded stability scope and less - conservative results can be obtained by the new method. Especially for some systems, which can not be analyzed by previous methods, the new method is always powerful to deal with them. Practical examples are given to verify the method and to illustrate its application.