The Lepschy stability test and its application to fractional-order systems

Abstract

It is shown how a stability test, alternative to the classical Routh test, can profitably be applied to check the presence of polynomial roots inside half-planes or even sectors of the complex plane. This result is obtained by exploiting the peculiar symmetries of the root locus in which the basic recursion of the test can be embedded. As is expected, the suggested approach proves useful for testing the stability of fractional-order systems. A pair of examples show how the method operates. It is believed that the suggested geometric approach can also be of some didactic value in introducing basic control-system tools to engineering students.

Keywords

• fractional-order systems
• d-stability
• recursive algorithms
• complex polynomials
• root locus
• symmetries
• control-theory didactics