Characteristic frequency functions and characteristic gain functions

Abstract

Abstract In the transform analysis of linear systems the two classical approaches use complex functions to study gain as a function of frequency (the Nyquist—Bode approach)and to study frequency as a function of gain (the Evans root locus approach)The central feature of any transform approach to the analysis of linear multivariable systems is the use of transfer-function matrices, and it. is the primary purpose of this paper to explain how the ideas of studying gain as a function of frequency, and frequency as a function of gain, can be extended to the multivariable case by associating with transfer-function matrices characteristic gain functions and characteristic frequency functions The characteristic gain function and characteristic frequency function are algebraic functions, each of which is defined on an appropriate Riemann surface. Considering the Riemann surface domain for the characteristic frequency function, a stability criterion for linear multivariable feedback systems is established which doe...