Exponential stability of fractional-order uncertain systems with asynchronous switching and impulses. (English) Zbl 1543.93288
Summary: Different from the Mittag-Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional-order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality \(E_{\alpha}(t)\leq\frac{1}{\alpha}\exp\left(t^{\frac{1}{\alpha}}\right)\) \(\left(0<\alpha<1\right)\), by utilizing the theory of fractional-order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less-conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with \(\alpha=1\) are also novel in contrast with the ones of integer-order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results.
© 2024 John Wiley & Sons Ltd.
© 2024 John Wiley & Sons Ltd.
MSC:
| 93D23 | Exponential stability |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 93C41 | Control/observation systems with incomplete information |
| 93C27 | Impulsive control/observation systems |
Keywords:
asynchronous switching and impulses; exponential stability; fractional-order uncertain systemsReferences:
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