Speaker Prof. Jian-Qiao Sun Professor, ASME Fellow School of Engineering University of California, Merced Abstract In this talk, several interesting applications of time delay of dynamical systems are discussed, including human gait, metal cutting on the lathe, and car following models. The recent results of analysis and control of time-delayed dynamical systems are presented. Some numerical methods for solutions of delayed differential equations (DDE) are reviewed, pointing out that several popular methods for analysis and control of dynamical systems with time delay can be formulated in the general framework of the abstract Cauchy problem for DDEs. We then present a continuous time approximation method and show its prediction power both in frequency and time domain. We also consider the stability ...