Review of Some Matrix Continued-Fraction Descriptions and Their Applications to the Stability of Multivariable Control Systems

摘要

A review is given of some aspects of the matrix continued-fraction approach to the theory of multivariable linear control systems, as developed by Shieh and various co-workers over the past decade. These basic matrix continued-fraction descriptions (MCFDs) associated with matrix fraction descriptions (MFDs) of a square transfer-function matrix are described. A matrix Euclidean algorithm and a matrix Sturm algorithm are developed, and applications made in the determination of the greatest common divisor of polynomial matrices, and the transformation between right and left irreducible MFDs. Using the relevant linear matrix equation obtained from Liapunov theory, the structure of the matrix equation obtained from Liapunov theory, the structure of the matrix continued-fraction description allows the derivation of various sufficient conditions for stability or instability of a class of linear control systems. Keywords: Control theory; Algorithms; Mathematical technique; Linear systems; Multivariable systems.