Nonlinear Dynamics

, Volume 85, Issue 1, pp 633–643 | Cite as

Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems

Original Paper


This article investigates a novel sliding model control approach for a class of nonlinear fractional order systems. In particular, the sliding surface with additional nonlinear part is designed by a Lyapunov-like function and one can achieve much more satisfying system performances by selecting suitable parameters. Moreover, a second-order switching law is generated from the commonly used adaptive switching law. Its properties are carefully discussed, and it is proven that the reaching time of the sliding surface can be guaranteed nonsensitive to the initial conditions with the second-order switching law, while the adaptive switching law cannot even guarantee the finite-time convergence. Then the stability of the closed-loop control system is rigorously analyzed via indirect Lyapunov method. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control method.


Fractional order systems Sliding mode control Second-order switching law Indirect Lyapunov method Frequency distributed model 


Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of AutomationUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Institute of Electronic EngineeringChina Academy of Engineering PhysicsMianyangChina

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