Control-Relevant Discretization of Nonlinear Systems With Time-Delay Using Taylor-Lie Series

A new time-discretization method for the development of a sampled-data representation of a nonlinear continuous-time input-driven system with time delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold 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. 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. 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 the case study of a two-degree-of-freedom mechanical system that exhibits nonlinear behavior. Various sampling rates and time-delay values are considered.