Exponential Stability for a Class of Fractional Order Dynamic Systems
The paper presents a comparinson of exponential, Mittag-Leffler and generalized Mittag-Leffler stability problems for a class of fractional order dynamical systems. The considered system is described by state equation with diagonal state matrix, the spectrum of the system contains single, separated, real, decreasing eigenvalues. An example of such a system is a heat object described by a fractional order state equation. The fractional order derivative is described by Caputo and Caputo-Fabrizio operators. For the considered system the simple conditions of approximated equivalence of the all discussed stabilities are proposed. Results are illustrated by the numerical example.
KeywordsFractional order systems Fractional order state equation Caputo operator Caputo-Fabrizio operator Exponential stability Mittag-Leffler stability Generalized Mittag-Leffler stability
This paper was sponsored by AGH UST project no 184.108.40.2067.
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