A tutorial on stability and stabilization of delay differential systems

The present paper gives an exposition of the Lyapunov direct method applied to obtaining stability criteria for time-delay systems, with a view to showing a recent result on the conservativeness brought about by model transformations. Applications of Lyapunov function is illustrated in an expository style, taking up linear system with a time-varying delay. The instability phenomena appears when a stabilizing derivative feedback control law is replaced by a difference counterpart. The approximation schemes possibly have a different robustness in preserving the closed-loop stability systems. Further a recent topic on approximate realization of a special class of stabilizing controllers is illustrated.