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Simultaneous Stabilization of Three or More Plants: Conditions on the Positive Real Axis Do Not Suffice

Authors :
R. Rupp
Raymond Mortini
Vincent D. Blondel
Michel Gevers
Source :
SIAM Journal on Control and Optimization. 32:572-590
Publication Year :
1994
Publisher :
Society for Industrial & Applied Mathematics (SIAM), 1994.

Abstract

The problem of the simultaneous stabilizability of a finite family of single-input, single-output time-invariant systems by a time- invariant controller is studied. The link between stabilization and avoidance is shown and is used to derive necessary conditions for the simultaneous stabilization of k plants. These necessary conditions are proved to be, in general, not sufficient. This result also disproves a long- standing conjecture on the stabilizability condition of a single plant with a stable minimum phase controller. The main result is to show that, unlike the case of two plants, the existence of a simultaneous stabilizing controller for more than two plants is not guaranteed by the existence of a controller such that the closed loops have no real unstable poles.

Details

ISSN :
10957138 and 03630129
Volume :
32
Database :
OpenAIRE
Journal :
SIAM Journal on Control and Optimization
Accession number :
edsair.doi...........b8273fdb0102476931cdf8e18dab7e97
Full Text :
https://doi.org/10.1137/s0363012991218815