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.
Simultaneous stabilization, linear systems, improper controllers
Abdallah, Chaouki T.; M. Bredemann; and Peter Dorato. "On the Relative Degree of Simultaneously Stabilizing Controllers." (2012). http://digitalrepository.unm.edu/ece_fsp/152