Time-discretization of state time delayed nonlinear systems via taylor lie series

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sample-data representation of a nonlinear system with constant state time-delay. The mathematical expressions of the discretization scheme are presented and the effect of the time-discretization method on key properties of nonlinear control system with state time-delay, such as equilibrium properties and asymptotic ability, is examined. The proposed scheme provides a finite-dimensional representation for nonlinear systems with state time-delay enabling existing controller design techniques to be applied to them. The performance of the proposed discretization procedure is evaluated using a nonlinear system.