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On the Relative Degree of Simultaneously Stabilizing Controllers

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/20443

On the Relative Degree of Simultaneously Stabilizing Controllers

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Title: On the Relative Degree of Simultaneously Stabilizing Controllers
Author: Abdallah, Chaouki T.; Bredemann, M.; Dorato, Peter
Subject(s): Simultaneous stabilization
linear systems
improper controllers
Abstract: In this brief paper 1 we present new necessary and sufficient conditions on the controller for the existence of a single controller to stabilize a set of n SISO plants: P1; P2; :::; Pn. As is well known this is equivalent to the existence of a single stable controller that stabilizes n - 1 plants (strong stabilization). It was shown in (Blondel, 1994) that the simultaneous stabilization problem is transcendental and cannot be solved using algebraic functions. Our only hope in approaching the general solution to the simultaneous stabilization problem using algebraic functions is either to enlarge the class of controllers for which sufficient conditions exist, or to restrict the class of controllers from which a controller must exist. This paper restricts the search for existence of simultaneously stabilizing controllers to the class of exactly proper controllers.
Date: 2012-04-26
URI: http://hdl.handle.net/1928/20443

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