The stability of the controlled problem of fuzzy dynamic systems involving the random-order Caputo fractional derivative. (English) Zbl 1536.93681
Summary: This article discusses the stability theory of fuzzy fractional dynamic systems with the random-order Caputo fractional derivative (RO-FFDSs). We establish new inequalities on the random-order Caputo fractional derivative, which is an essential tool in investigating the stability theory of RO-FFDSs. Based on the extension of the Lyapunov direct method (LDM), we investigate the asymptotical stability (AS) and the Mittag-Leffler stability (MLS) of the controlled problem of RO-FFDSs via a linear feedback controller. Finally, numerical examples are given to show the effectiveness of the theoretical results.
MSC:
| 93D20 | Asymptotic stability in control theory |
| 93C42 | Fuzzy control/observation systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
Keywords:
fuzzy fractional dynamic systems; Caputo fractional derivative; random-order fractional derivative; random-order fractional Lyapunov method; Mittag-Leffler stability; asymptotical stabilityReferences:
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