## Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach.(English)Zbl 1165.34408

Summary: A stability test procedure is proposed for linear nonhomogeneous fractional order systems with a pure time delay. Some basic results from the area of finite time and practical stability are extended to linear, continuous, fractional order time-delay systems given in state-space form. Sufficient conditions of this kind of stability are derived for particular class of fractional time-delay systems. A numerical example is given to illustrate the validity of the proposed procedure.

### MSC:

 34K20 Stability theory of functional-differential equations 26A33 Fractional derivatives and integrals

### Keywords:

stability analysis; time-delay systems; fractional calculus
Full Text:

### References:

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