Discretization of Delayed Multi-input Nonlinear System via Taylor Series and Scaling and Squaring Technique

Abstract

A new discretization method for the calculation of a sampled-data representation of nonlinear continuous-time system is proposed. The suggested method is based on the well-known Taylor-series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear system with time-delayed multi-input is derived. First the new approach is applied to nonlinear systems with two inputs. And then the delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 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 sampling rates. Practical issues associated with the selection of the method’s parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time-delay: maneuvering an automobile.