An algebraic algorithm for determining the desired gain of multivariable feedback systems

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Abstract
In this paper an algebraic method is presented whereby one can obtain the relevant values of the gain, K, of a multivariable (multi-input-multi-output) feedback system to be stable or relatively stable. The basis of the method involves the algebraic solution of the two equations obtained from the real and imaginary parts of the characteristic equation of the system. The proposed method offers an alternative procedure for determining stability (relative stability) to the graphical methods based on the ‘ generalized Nyquist criterion ’ and the ‘ multivariable root locus method ’. This method is analogous to the analytical form of the root locus combined with the Routh-Hurwitz criterion, as compared to the Nyquist or graphical root locus methods when applied to single-input-single-output feedback systems. Several examples are presented illustrating the applications of the method and compared with the graphical methods.

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