Discrete time normal form for the left invertibility problem

Abstract

This paper deals with the discrete time left invertibility problem. It is directly related to the design of observer for nonlinear systems with unknown input, which has many applications in cryptography. In this paper, a normal form for the left invertibility problem is established in the linearly observable case, thanks to an extended output injection. Then, an algorithm for the normal form computation will be proposed for the linearly unobservable case. The deduced equivalence class is generalized to any approximation order. Finally, the paper ends with an illustrative example.