Efficient Computation Method for Strong Stability Area of Neutral Equations

A reliable method for the computation of the strong stable area of neutral delay differential equations is presented. A special neutral system with commensurate delays is analysed. Phase parameters are used to determine all possible parameter points where a critical characteristic root may occur for a given time delay ratio. An extra condition is formulated to define the boundary curves of the robust stable area. The corresponding co-dimension 3 parameter problem in the 4 dimensional parameter space is solved efficiently by the MultiDimensional Bisection Method. Finally the so-called instability gradients are used to classify the distinct domains of the chart. It is shown, that the computational time of the proposed method to obtain the strong stable area is comparable to the CPU time needed for the computation of the stability chart for a given fixed delay ratio.