CONSTRAINED CONTROLLABILITY OF LINEAR DISCRETE NONSTATIONARY SYSTEMS IN BANACH-SPACES

This paper studies local null-controllability of linear infinite-dimensional, nonstationary, discrete-time systems of the form x(k+1) = A(k)x(k) + B(k)u(k), u(k) is-an-element-of OMEGA subset-of U, x(k) is-an-element-of M(k) subset-of X, where X, U are Banach spaces; A(k), B(k) are linearbounded operators; M(k), OMEGA are given nonempty subsets. New necessary and sufficient conditions for local null-controllability are given. The main tool is the surjectivity theorem for convex multivalued mappings in Banach spaces.