A unified structural interpretation of some well-known stability-test procedures for linear systems

Creators: Vaidyanathan, P. P.; Mitra, Sanjit K.

Abstract

A number of well-known stability-test procedures for continuous-and discrete-time systems are re-examined in a unified manner, leading to well-defined network-theoretic interpretations. The representation and network interpretation are based on the fact that the stability of any linear system (scalar or multivariable) is equivalent to the stability of a related all-pass system, which in turn can always be synthesized as a cascade of (scalar or matrix) two-pair all-pass (lossless) networks. The original system of interest is stable if and only if each all-pass two-pair is stable (and hence "lossless bounded real"). As a result of this interpretation, a number of related issues, such as enumeration of unstable poles, prematured terminations, and singularity situations can all be approached in a unified manner, based only on "two-pair extraction formulas." In addition, the network interpretation also leads to direct test procedures for testing relative stability, and the stability of multi-input, multi-output systems.

Additional Information

© Copyright 1987 IEEE. Reprinted with permission. Manuscript received March 18, 1985; revised March 14, 1986. The authors wish to thank Prof. E.I. Jury of the University of Miami, Coral Gables, FL, and Prof. Y. Neuvo of the Tampere University of Technology, Tampere, Finland, for useful comments and encouragements. The comments and suggestions by the anonymous reviewers are also gratefully acknowledged. This work was supported in part by the National Science Foundation under Grants DCI-850817 and ECS-8404245.

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