On the Relative Degree of Simultaneously Stabilizing Controllers

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

Strong Simultaneous Stabilization Of Siso Plants

In this brief paper 1 we present sufficient conditions for the existence of a single stable controller to stabilize a set of n plants: P 1 ; P 2 ; :::; P n (strong simultaneous stabilization). As is well known this is equivalent to the existence of a single controller, not necessarily stable, to stabilize n + 1 plants (simultaneous stabilization). The basic assumption required in the current paper is that all the plants have the same unstable zeros. A practical example of where such an assumption holds, is when each plant has the same pure delay which is approximated by a non-minimum phase rational function. The results here are applied to examples of this type. Key Words. Simultaneous stabilization, linear systems, interpolation algorithm. 1 This paper was first presented at the IFAC Symposium on Robust Control Design, Rio De Janeiro, 14--16 September, 1994. 1 INTRODUCTION The problem of stabilizing n + 1 different plants is a longstanding problem in the robust control literatu..