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