Transcendental and interpolation methods in simultaneous system design

Let us begin by asking ourselves the following question - "Does there exist three single input single output proper plants of degree 1 with the property that every pair of plants in the above triplet is simultaneously stabilizable by some dynamic compensator but the triplet is simultaneously unstabilizable by any dynamic compensator." Of course the above question is primarily of theoretical interest; however, it illustrates one of the salient features of the simultaneous stabilization problems which we now explain.