Control-relevant discretization of nonlinear systems with time-delay using Taylor-Lie series

A new time-discretization method for the development of a discrete-time (sampled-data) representation of a nonlinear continuous-time control system with time-delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization scheme is explored and characterized as useful for establishing concrete connections between numerical and system-theoretic properties. The effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. The resulting time-discretization provides a finite-dimensional representation for nonlinear control systems with time-delay enabling the application of existing controller design techniques. The performance of the proposed discretization procedure is evaluated using a case study.