摘要：AbstractTime-delay systems with delay-dependent coefficients arise from different disciplines, but methods and algorithms for stability analysis of this kind of systems are very few compared with the intensive ones for time-delay systems with delay-free coefficients. This paper presents three algorithms for calculating the spectral abscissa of these time-delay systems with the delay as a parameter, an index that determines the stability and the decaying rate of the systems. The key step of the proposed algorithms is the use of parametric continuation method to calculate the real part branches by solving initial value problems of an ordinary differential equation derived from the characteristic function, where the initial values of the initial value problems are chosen as the rightmost characteristic roots, or the second rightmost characteristic roots, and so on, and they are calculated by using the integration-based-stability-test method. The algorithms are particularly effective when the delay interval is short.
