Linear nonstationary control systems: Null-controllability with restrained controls in Banach spaces

In this paper are given new necessary and sufficient conditions for the local null-controllability of the nonstationary discrete-time systems xkÅ+1=Akxk+Bkuk, uk∈¦[ℝU, xk∈X, where X, U are infinite-dimensional Banach spaces. The proof of the main results is based on the theorem on the implicit function for the set-valued mapping. An application to non-stationary continuous-time systems with restrained controls is also given.