Abstract
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 conditions 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 deployment with fractional-order control law.
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