A digital signal processing perspective on a stability test of linear system transfer functions

The stability of a linear transfer function is fundamental in its real time realisation. Several tests have been developed in the past to test whether a given transfer function is stable. Invariably these tests rely on either a direct use of a Hurwitz test or some convenient modification of it such as the Schur-Cohen test or the Jury-Marden test. A new test is proposed in this contribution which does not rely on the same principles but on the Cauchy integral, and its implementation in practice requires merely the use of the Fast Fourier Transform. The test is convenient for real time implementation.