On Mikhailov Stability Conditions for a Class of Integer- and Commensurate Fractional-Order Discrete-Time Systems

The Mikhailov stability condition is a classical stability test for continuous-time systems, similar to the well-known Nyquist method. However, in contrast to the Nyquist criterion, the Mikhailov stability tests do not reach considerable research attention. This paper introduces an extension of Mikhailov stability condition for two classes of a discrete-time system in terms of linear time-invariant system, and fractional-order one based on ‘forward-shifted’ Grünwald-Letnikov difference. Simulation experiments confirm the usefulness of the Mikhailov methods for stability analysis of discrete-time systems.