On local controllability of nondifferentiable discrete-time system with nonconvex constraints on controls

In this paper a sufficient condition for local controllability of discrete-time systems of the following form will be established: xkÅ+1=fk(xk,uk), xk∈Rⁿ, uk∈¦[k, k=0,1,...,m-1, where ¦[k (k=0,1,...,m-1) are closed subsets of R^r and fk: Rⁿ×R^r∈Rⁿ are locally-Lipschitz functions. Some corollaries including a controllability condition for linear discrete-time systems with nonconvex constraints on controls are also obtained.