Algebraic phase unwrapping and zero distribution of polynomial for continuous-time systems (Q2702520)

The aim of the paper is to provide an analytic solution to the phase unwrapping problem of continuous-time linear time-invariant systems. This problem is closely related to the problem of determining the zero distribution of a given univariate complex polynomial with respect to the imaginary axis in the complex plane. The obtained solution is shown to lead to algorithms that are guaranteed to terminate in less than a known finite number of steps, thus avoiding the plethora of singular cases that are encountered in all Euclidean division-based algorithms.NEWLINENEWLINENEWLINEThe authors investigate the implications of the new approach to the zero-distribution problem for a univariate complex coefficient polynomial based on the generalized Sturm sequence, on the test problems for multivariate polynomial positivity, and on the multidimensional filter stability.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00062].