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A criterion on the asymptotic stability of fractional-order systems withincomensurate orders is proposed in this paper. Existing methods always assumeorder parameters be rational numbers or the ratios of any two orders berational numbers. In engineering applications, order parameters are more likelyto be uncertain which may be real numbers. Furthermore, the boundary of thestable parameter region is determined, which decomposes parameter space intothe finite number of connected regions. All systems whose parameters belong tothe same region have the same stability. Each region only needs checking onepoint to determine the stability of the region. The method established in thispaper involves low computational complexity and clearly gives the relationshipbetween order parameters and stability. Some examples show the advantages ofthis method.

A criterion for asymptotic stability of general fractional-order linear time-invariant systems with incommensurate orders