Delay-dependent and order-dependent asymptotic stability conditions for Riemann-Liouville fractional-order systems with time delays. (English) Zbl 1524.34180
Summary: In this paper, the asymptotic stability problem for Riemann-Liouville fractional-order systems with time delays is investigated. First, a new Lyapunov theorem for asymptotic stability is proved. Then, based on the Lyapunov theorem and fractional-order Jensen inequalities, two delay-dependent and order-dependent conditions for asymptotic stability of Riemann-Liouville fractional-order systems are derived by constructing new classes of Lyapunov functions. The derived criteria are described in terms of linear matrix inequalities, which are computationally efficient. Finally, an example is provided to demonstrate the effectiveness and less conservativeness of the proposed results.
MSC:
| 34K20 | Stability theory of functional-differential equations |
| 34K37 | Functional-differential equations with fractional derivatives |
Keywords:
fractional-order system; time-delay system; fractional-order integral inequality; Riemann-Liouville fractional-order derivativeReferences:
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