Remarks of discretization and linear equivalence of continuous time nonlinear systems

We investigate the effect of sampling on linear equivalence for continuous time systems. It is shown that the discretized system is linearizable by state coordinate change for an open set of sampling times if and only if the continuous time system is linearizable by state coordinate change. Also, for n=2, we show that even though the discretized system is linearizable by state coordinate change and feedback, the continuous time affine complete analytic system is linearizable by state coordinate change only. Also, we suggest a method of proof when n ≥ 3.