Stability test procedure for a certain class of the fractional-order systems

Abstract

This papers deals with the stability test procedure for a certain class of the fractional-order systems. The proposed approach is based on the Nyquist stability criterion. The fractional-order systems can be described by the fractional-order differential equations or by fractional-order transfer functions. This approach does not need the poles calculation of the close-loop system characteristic equation, which is not polynomial but so-called pseudopolynomial with fractional power. The proposed test procedure is demonstrated on several illustrative examples. By using a Matlab function solve(), the obtained stability results are cross-validated. The other criteria for stability investigation are discussed in conclusion of article.