Simultaneous Partial Pole Placement: A New Approach to Multimode System Design

Simultaneous partial pole placement of a family of single-input single-output plants is proposed as a generalization of the classical Pole placement and stabilization problems. This problem finds application in the design of a compensator for a family of linear dynamical systems. In this note we show that the proposed problem is equivalent to a new class of transcendental problem using stable, minimum phase rational functions with real coefficients. A necessary condition for the solvability of the associated transcendental problem is obtained. Finally, a counterexample to the following conjecture is obtained—“pairs of simultaneously stabilizable plants of bounded McMillan degree have simultaneously stabilizing compensators of bounded McMillan degree.”