ON STABILITY OF A CLASS OF CONTROLLED DISCRETE-TIME SYSTEMS IN HILBERT SPACE

摘要

A class of discrete-time state operators on a Hilbert space is exhibited as a concrete instance of systems having power-bounded operators that are not, similar to contractions albeit the state operators are asymptotically stable. It is shown that such discrete-time systems arise from sampled feedback control of unstable continuous-time systems. This result is obtained as a consequence of the particular structure of the spectrum of the state operator and the control input operator.