Internal Stabilization of Coherent Control Systems

We give a necessary and suÆcient condition so that a system is internally stabilizable and we prove that any system de ned by a transfer matrix with entries in the eld of fractions K = Q(A) of A is internally stabilizable if and only if A is a Pr ufer domain. Hence, if A is a Pr ufer domain which is not a B ezout domain, then there exist some internal stabilizable plants which have no doubly coprime factorizations. Moreover, we show that if the ring A is a Hermite ring, then it is possible to parametrize all the stabilizing controllers of an internally stabilizable plant by means of the Youla parametrization. Finally, our approach of synthesis problems, based on algebraic analysis [13], allows to recover in a unique framework the di erent results obtained in [9,10,15,16]. Copyright C 2001 IFAC.