A Sufficient Condition for Simultaneous Stabilization

Blondel, Vincent;Campion, Guy;Gevers, Michel
(1993) IEEE Transactions on Automatic Control — Vol. 38, n° 8, p. 1264-1266 (1993)

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  • Blondel, Vincentorcid-logoUCLouvain
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  • Campion, GuyUCLouvain
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  • Gevers, MichelUCLouvain
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Abstract
In this note, we study the following problem, ''Under what condition(s) is it possible to find a single controller which stabilizes k single-input single-output linear time-invariant systems p(i)(s) (i = 1, ..., k)?''. We introduce the concept of avoidance in the complex plane and use it to derive a sufficient condition for k systems to be simultaneously stabilizable. A method for constructing a simultaneous stabilizing controller is also provided and illustrated by an example.
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Blondel, V., Campion, G., & Gevers, M. (1993). A Sufficient Condition for Simultaneous Stabilization. IEEE Transactions on Automatic Control, 38(8), 1264-1266. https://doi.org/10.1109/9.233164 (Original work published 1993)