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Sufficient stability condition for fractional-order nonlinear systems

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Abstract

This study examines the stabilization control problem for Fractional-order nonlinear systems (FONS). Based on the frequency distribution model of the fraction-order integrator, a sufficient stability condition is presented for the Riemann-Liouville FONS. The stability of the FONS is proven using Lyapunov stability theory. An improved sufficient stability condition is also proposed with Linear matrix inequalities (LMIs) techniques. A novel control law to stabilize the FONS is put forward. Numerical simulation examples are provided to verify the proposed approaches.

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Northeast Petroleum University, Daqing, 163318, China

    Keyong Shao

  2. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, 710072, China

    Lei Zuo

Authors
  1. Keyong Shao
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  2. Lei Zuo
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Corresponding author

Correspondence to Keyong Shao.

Additional information

Recommended by Associate Editor Yang Shi

Keyong Shao is currently a Pofessor in School of Electrical and Information Engineering, Northeast Petroleum University. He was born in Huainan, Henan Province, China in 1970. He received his B.E. degree from Daqing Northeast Petroleum Institute in 1992, his M.E. degree from Northeast University, Shenyang, China, in 2000, his Ph.D. in Control Theory and Control Engineering from Northeast University, Shenyang, China, in 2003. His main research interests include robust control and fractional-order system theory.

Lei Zuo is currently a Ph.D. candidate in School of Marine Science and Technology, Northwestern Polytechnical University, China. He received his B.Eng. degree from NWPU in 2011 and directly began his Ph.D. program in Control Theory and Control Application. He is interested in adaptive control, coverage control and optimization. His current research interests are focus on the coverage control for underwater vehicles in unknown environment.

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Shao, K., Zuo, L. Sufficient stability condition for fractional-order nonlinear systems. J Mech Sci Technol 31, 3531–3537 (2017). https://doi.org/10.1007/s12206-017-0641-z

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  • DOI: https://doi.org/10.1007/s12206-017-0641-z

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