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Mittag-Leffler Stability of Fractional-Order Nonlinear Differential Systems With State-Dependent Delays

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The stability of fractional-order (FO) nonlinear system with state-dependent delays (SDDs) is investigated. Unlike the usual time-dependent delays, the state-dependent (SD) delays make the size of the delays relative to… Click to show full abstract

The stability of fractional-order (FO) nonlinear system with state-dependent delays (SDDs) is investigated. Unlike the usual time-dependent delays, the state-dependent (SD) delays make the size of the delays relative to the states, which makes the system uncertain when historical state information would be used. A Lemma on Riemann-Liouville derivative is first given to ensure the monotonicity of the considered function. Then, based on the Lyapunov method, several sufficient criteria are presented to guarantee the Mittag-Leffler stability of the discussed systems. In the end, three examples are applied to illustrate the correctness and applicability of our theoretical conclusions, including practical applications in submarine positioning models.

Keywords: state; state dependent; stability fractional; fractional order; dependent delays

Journal Title: IEEE Transactions on Circuits and Systems I: Regular Papers
Year Published: 2022

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