Stability of a class of multivariable control systems described by nested matrix continued-fractions

Abstract

This paper deals with the stability of a class of multivariable control systems which can be described by a right (left) matrix fraction description and associated right (left) matrix continued-fraction description in the nested Cauer form. Some simple sufficient conditions and some simple necessary conditions are developed for stability determination of the class of multivariable systems via the Lyapunov stability and instability theorems. By simple testing of the (positive or negative) definiteness of a set of matrix quotients obtained from the matrix Sturm algorithms, the stability of the class of multivariable systems can be determined. The matrix fraction descriptions of interest may be unsymmetric and reducible.