| Summary: | 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.
|
|---|
