Constructible Canonical Form and High-gain Observer in Discrete Time

This work presents a triangular form that is shown to be canonical for constructible discrete-time systems. For this form, we propose an observer that resembles the wellknown high-gain observer in continuous time. This discrete-time observer exhibits exponential stability if its dynamics are picked sufficiently fast, as well as robustness against disturbances and measurement noise. We also study how to transform general discrete-time systems into this constructible form, under constructibility and backward distinguishability, and recover convergence in the given coordinates. Application to an electrical machine with comparison to the discretized version of the continuous-time high-gain observer illustrates our methods.