Exact sampled data representation of continuous time nonlinear systems by finite polynomials with exactly determined coefficients

A new time discretization scheme is presented, based on a Taylor series expansion of the continuous time nonlinear system. It is shown that any Taylor series coefficient of the corresponding discrete-time nonlinear system can be calculated exactly. Therefore, the notion of Lie sequences is introduced facilitating the calculation of Taylor-Lie series significantly. Since the resulting coefficient can be expressed in terms of the matrix exponential, numerical algorithms for the determination of each coefficient can be used. An illustrative example quantifies the results.