Circuits, Systems, and Signal Processing

, Volume 36, Issue 1, pp 65–81 | Cite as

On the Robust Stability of Active Disturbance Rejection Control for SISO Systems

  • Xiaohui Qi
  • Jie Li
  • Yuanqing Xia
  • Zhiqiang Gao


Active disturbance rejection control (ADRC) is a new practical control technique, which can integrally and effectively deal with various nonlinearities, uncertainties and disturbances (collectively called the total disturbance throughout this paper). This paper addresses the problem of the robust stability analysis and design of linear and nonlinear ADRC for SISO systems. Firstly, a nonlinear ADRC-based control system with total disturbances is transformed into a perturbed indirect Lurie system. Then, the Popov–Lyapunov method is used to study its global or local stability and derive the robust stability bound on allowable total disturbance. Furthermore, if the total disturbance of the system is known, an estimated region of attraction can be obtained. In addition, the paper illustrates how the modeled linear dynamics can be easily integrated into ADRC to improve both the performance and stability characteristics. The above approach can also be extended to a linear ADRC-based control system. A numeral example is presented to verify the convenience and practicability of the proposed method.


Active disturbance rejection control Lurie system Robust stability Popov criterion Region of attraction 



The authors would like to thank the referees for their valuable and helpful comments which have improved the presentation. The work was supported by the open funding program of Joint Laboratory of Flight Vehicle Ocean-Based Measurement and Control under Grant No. FOM2015OF011, the National Basic Research Program of China (973 Program) under Grant No. 2012CB720000, the National Natural Science Foundation of China under Grant No. 61225015 and Grant No. 61105092 and Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant No. 61321002.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Xiaohui Qi
    • 1
  • Jie Li
    • 1
  • Yuanqing Xia
    • 2
  • Zhiqiang Gao
    • 3
    • 4
  1. 1.Department of Unmanned Aerial Vehicle EngineeringMechanical Engineering CollegeShijiazhuangChina
  2. 2.School of AutomationBeijing Institute of TechnologyBeijingChina
  3. 3.Center for Advanced Control TechnologiesCleveland State UniversityClevelandUSA
  4. 4.Tianjin University of TechnologyTianjinChina

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