On robust stability of incommensurate fractional-order systems

This paper investigates the robust stability of fractional-order systems described in pseudo -state space model with incommensurate fractional orders. An existing non-conservative robust stability criterion for integer-order systems is extended to incommensurate-order fractional systems by using the generalized Nyquist Theorem. Some robust stability condi-tions for various uncertainty structures are proposed by employing the proposed criterion. Moreover, we focus on the interval uncertainty structure to discuss the conservatism of the common methods. A numerical example is provided to investigate that how the fractional-order of each pseudo-state can affect the robustness of the system. The effectiveness of the proposed methods is compared by applying them on the problem of space tether deploy-ment with fractional-order control law. (C) 2020 Elsevier B.V. All rights reserved.