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

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.