A method of continuous time approximation of delayed dynamical systems

This paper presents a new method to analyze response of linear and nonlinear dynamical systems with time delay. The method proposes a continuous time approximation of the delayed portion of the response. This leads to a high and finite dimensional state space formulation of the time-delayed system. The advantage of the current method lies in that the resulting finite dimensional state equations are in the standard state space form, making all the existing analysis methods and control design tools for linear and nonlinear dynamical systems amenable to the current approach. The method can also handle multiple independent time delays in a natural way. One- and two-dimensional dynamical systems with time delay are used to demonstrate the effectiveness of the method.