Journal
NONLINEAR DYNAMICS
Volume 80, Issue 1-2, Pages 51-58Publisher
SPRINGER
DOI: 10.1007/s11071-014-1850-y
Keywords
Fractional-order systems; Sliding-mode control; Linear matrix inequalities; Sliding-mode surface
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Funding
- National Natural Science Funds of China for Distinguished Young Scholar [50925727]
- National Natural Science Funds of China [61403115, 61374135]
- National Defense Advanced Research Project Grant [C1120110004]
- Chinese Ministry of Education [313018]
- Anhui University [KJJQ1102]
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The problem of designing a sliding-mode controller for a class of fractional-order uncertain linear perturbed systems with Caputo derivative is addressed in this paper. Sufficient conditions for the existence of sliding surfaces guaranteeing the asymptotic stability of the reduced-order sliding-mode dynamics are obtained in terms of linear matrix inequalities, based on which and stability theory of fractional-order nonlinear systems; the corresponding reaching motion controller is proposed, and the reaching time is also obtained. Moreover, the upper bounds of the nonlinear uncertainties are not required to be known in advance, which can be tuned by the designed adaptive law. Meanwhile, some problems for the sliding-mode controller for fractional-order systems in existing literatures are pointed out. A numerical example is presented to demonstrate the validity and feasibility of the obtained results.
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