Improvements of Routh Algorithm and Jury Criterion and Their Applications to Stability Analysis and Design of Linear Systems

• Main Authors: Shyan-Shyi Chen, 陳賢錫
• Other Authors: Jason S. H. Tsai
• Format: Others
• Language: zh-TW
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/32800878921013916953

博士 === 國立成功大學 === 電機工程研究所 === 81 === The purpose of this dissertation is to discuss and further investigate the most famous and convenient algorithm --- the Routh algorithm, for determining stability. In particular, modified procedures are developed to treat singular cases. The information of simple and repeated roots with respective orders will be obtained; therefore, one can distinguish the situation of conditional stability or instability. The extended Routh algorithm is developed to be applicable to more kinds of regions. The original Routh table dealing with the root distribution of a real polynomial is extended for the case of a complex polynomial. A new tabular form for determining the root distribution of a complex polynomial with respect to the imaginary axis is proposed based on the original Routh algorithm. Based on the tabular form proposed by Parks, modified procedures for treating singular cases are also proposed. Concerning a linear discrete system, the Jury table is the most famous one for determining the root distribution with respect to the unit circle. Efficient procedures are developed in this dissertation to overcome the singular cases of the Jury algorithm. Theorems for obtaining the information of simple and repeated roots on the unit cicrle with their respective orders are also proposed. To extend the applications of the Routh algorithm to the area of multivariable systems, we discuss matrix Routh algorithm widely. Based on the general one of the matrix Routh algorithm -- the matrix continued- fraction algorithm, problems in the research area of multivariable systems are investigated.