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IMA Journal of Mathematical Control and Information 1985 2(1):1-23; doi:10.1093/imamci/2.1.1
© 1985 by Institute of Mathematics and its Applications
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A Review of Some Matrix Continued-Fraction Descriptions and Their Applications to the Stability of Multivariable Control Systems

LEANG S. SHIEH{dagger}, YIH T. TSAY{ddagger} and S. BARNETT§

{dagger}Department of Eectrical Engineering, University of Houston - University Park Houston, Texas 77004, USA.
{ddagger}Department of Computer Science, University of Houston - University Park Houston, Texas 77004, USA.
§School of Mathematical Sciences, University of Bradford West Yorkshire BD7 1DP, England.

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 Sturni algorithm are developed, and applications made in the determina tion of the greatest common divisor of polynomial matrices, and the transforma tion between right and left irreducible MFDs. Using the relevant linear 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.


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