Robust D-Stability Criterion for Fractional Order Systems with Uncertainties in Both the Coefficients and Orders

This paper investigates the robust D-stability criterion of fractional order systems with parametric uncertainties. Uncertainties are considered in the both coefficients and orders of the fractional order systems. To this end, some bounds on the roots of fractional order polynomials are obtained, helping to examine the robust D-stability criterion. Then, by using the zero exclusion principle a necessary and sufficient criterion to check the robust D-stability is presented. The obtained results can be applied to fractional order systems of both commensurate and incommensurate orders. One numerical example is given to verify the results.

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