Approximate and local linearizability of non-linear discrete-time systems

Abstract
We consider a single-input non-linear discrete-time system of the form where x ϵℝN, uϵℝ, and f(x,u): ℝN+1 → ℝN is a CN - valued function. Necessary and sufficient conditions for approximate linearizability are given for Σ. We also give necessary and sufficient conditions for local linearizability. Finally, we present analogous results for multi-input non-linear discrete-time systems.