Stabilization on Null Controllable Region

  • Hongjiu Yang
  • Yuanqing Xia
  • Qing Geng
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 193)


A set of equilibrium points in a null controllable region is obtained based on an important assumption. A stable equilibrium line is given for DOSs subject to actuator saturation . A complex controller is constructed to achieve global stabilization of DOSs with actuator saturation . Our motivation is to get simpler structures of controllers such that the controllers are less sensitive to uncertainties and disturbances of system models than the ones for global stabilization. Therefore, a simple controller is designed to obtain semi-global stabilization of DOSs with actuator saturation . Note that the null controllable region has not been considered in [163]. Moreover, neither global nor semi-global stabilization of states in the null controllable region has not been investigated in [163]. Stabilizability plays a crucial role in all control systems , such as switched linear systems , NCSs , T-S fuzzy stochastic systems, and invertible multi-input multi-output nonlinear systems . Note that high gain feedbacks are essential for semi-global and global stabilization of continuous-time systems subject to actuator saturation. Contrary to continuous-time systems , a high gain feedback taken to research stabilization of discrete-time systems subject to actuator saturation is completely different. In fact, the high gain feedback in discrete-time systems is usually destabilizing. Therefore, a research of the DOSs with actuator saturation is necessary to solve this issue.


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    H. Yang, P. Shi, Z. Li, C. Hua, Analysis and design for delta operator systems with actuator saturation. Int. J. Control 87(5), 987–999 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Hongjiu Yang
    • 1
  • Yuanqing Xia
    • 2
  • Qing Geng
    • 3
  1. 1.School of Electrical and Information EngineeringTianjin UniversityTianjinChina
  2. 2.School of AutomationBeijing Institute of TechnologyBeijingChina
  3. 3.Institute of Electrical EngineeringYanshan UniversityQinhuangdaoChina

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