, Volume 5, Issue 3, pp 371-387

A note on the genericity of simultaneous stabilizability and pole assignability

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In this paper we study the genericity of simultaneous stabilizability, simultaneous strong stabilizability, and simultaneous pole assignability, in linear multivariable systems. The main results of the paper had been previously established by Ghosh and Byrnes using state-space methods. In contrast, the proofs in the present paper are based on input-output arguments, and are much simpler to follow, especially in the case of simultaneous and simultaneous strong stabilizability. Moreover, the input-output methods used here suggest computationally reliable algorithms for solving these two types of problems. In addition to the main results, we also prove some lemmas on generic greatest common divisors which are of independent interest.

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant Number A-1240.
This work was supported in part by The Army Research Office under Grant Number BAAG29-84-K-0005.
This work was partially supported by the Department of Electronics, Government of India.