Time-discretization of nonlinear control systems via Taylor methods

A new discretization method for the calculation of a sampled-data represent ation of a nonlinear continuous-time system is proposed. It is based upon t he well-known Taylor method and the zero-order hold (ZOH) assumption. The m athematical structure of the new discretization scheme is analyzed and char acterized as being particularly useful in establishing concrete connections between numerical properties and system-theoretic properties. In particula r, the effect of the Taylor discretization procedure on key properties of n onlinear systems, such as equilibrium properties and asymptotic stability, is examined. Within a control context, numerical aspects of Taylor discreti zation are also discussed, and 'hybrid' discretization schemes, that result from a combination of the 'scaling and squaring' technique with the Taylor method, are also proposed, especially under conditions of very low samplin g rates. Practical issues associated with the selection of the method's par ameters to meet CPU time and accuracy requirements, are examined as well. F inally, the performance of the proposed discretization procedure is evaluat ed in a chemical reactor example, that exhibits nonlinear behavior and is s ubject to various sampling rates. (C) 1999 Elsevier Science Ltd. All rights reserved.