A Note on Complete Controllability and Stabilizability for Linear Control Systems in Hilbert Space

摘要

The linear control system dx/dt = Ax + Bu is considered. Here is A is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators T(t) on a Hilbert space E, B is a bounded linear operator from a Hilbert space H to E. Sufficient conditions are given for the existence of a bounded linear operator K from E to H so that the control system with feedback control law u(t) = Kx(t) has the zero solution asymptotically stable. In particular, the relationship between the concept of complete controllability and the existence of K is discussed. (Author)