Stability Analysis of Linear Delay Systems

From the viewpoint of mathematicians, the stability problem of a linear delay dynamic system has been solved because a number of sufficient and necessary conditions have been available for the stability analysis when the time delays are given. See, for example, (Stepan 1989), (Qin et al. 1989) and (Hassard 1997). As presented in Section 2.2, however, these conditions do not show any explicit relationship among the system parameters that the engineers are interested in. When those conditions are used, the stability test usually involves very tedious computation such as solving transcendental equations or computing the spectrum of operators.