NULL CONTROLLABILITY WITH VANISHING ENERGY FORDISCRETE-TIME SYSTEMS IN HILBERT SPACE

摘要

In this paper null controllability with vanishing energy is considered for discrete-time systems in Hilbert space. As in the case of continuous time systems, necessary and sufficientconditions in terms of an algebraic Riccati equation are given. Then necessary and sufficient condi-tions involving the spectrum of the system operator are given. Reachability and controllability withvanishing energy are also considered, and necessary and sufficient conditions for them are given.Finally applications to sampled-data systems, systems with impulse control, and periodic systemsare discussed.