ABSTRACT
By Lemma 7.2. 1 . 1 (b), the plants P and (1 - b.)P are simultaneously R-stabilizable if and only if there exists Q E M (R) such that condition 2.5 holds. It follows from standard strong R-stabilizability results that condition 2.5 holds if and only if the pair (I - U b.N, Db.N) satisfies the well-known parity-interlacing-property [ 1 , 17, 1 8] , which is equivalent to Lemma 7.2. 1 . 1 (c). However, condition 2.5 is not explicit, and the equivalent conditions in terms of the blocking U-zeros of (Db.N) require the entire list of such zeros on the real-axis. We now search for explicit conditions in terms of the poles of the given plant P and the known multiplicative perturbation b. for simultaneous R-stabilizability of the plants P and (I - b.) P. Lemma 7.2. 1 . 1 (c) immediately leads to the following necessary conditions.
