A local approach to the stabilization of linear systems defined over non-commutative normed *-algebras

We define below a notion of local stabilizability for systems whose coefficients lie in a C*-algebra, and we show that such a system is stabilizable if and only if it is locally stabilizable. The C*-algebra is not assumed to be commutative. Since B(H) is a C*- algebra, the results of this paper apply in particular to any system whose coefficients can be represented as bounded linear operators on some Hilbert space H.