Computation of Unstable Characteristic Roots of Neutral Delay Systems

We present an algorithm based on the argument principle for computing all unstable characteristic roots of a class of neutral time delay systems. By consecutively subdividing a bounded rectangular or half circular region on the right half complex plane into smaller ones, initial approximate positions of all unstable roots can be located efficiently. With these approximate positions as starting points for Newton's method, approximations for all roots are refined iteratively. The performance of the algorithm is shown by an example.