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Simultaneous stabilization of three or more plants: conditions on the positive real axis do not suffice. (English) Zbl 0825.93682

Summary: 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.

MSC:

93D15 Stabilization of systems by feedback
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