Circuits, Systems and Signal Processing

, Volume 5, Issue 3, pp 371-387

First online:

A note on the genericity of simultaneous stabilizability and pole assignability

  • M. VidyasagarAffiliated withDepartment of Electrical Engineering, University of Waterloo
  • , B. C. LevyAffiliated withLaboratory for Information and Decision Systems, Massachusetts Institute of Technology
  • , N. ViswanadhamAffiliated withSchool of Automation, Indian Institute of Science

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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.