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Saturation-Dependent Lyapunov Function

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

Abstract

There are lots of methods to reduce conservatism in estimation of the DoA . Set invariance conditions for singular linear systems subject to actuator saturation have been given in [74]. Output feedback stabilization of linear systems with actuator saturation has been considered in [143]. Stable actuator saturation compensators have been designed in frequency domain [12]. Some methods of estimating the DoA and properties of null controllable regions have been presented for continuous-time and discrete-time systems with actuator saturation . The majority of the methods are mainly based on a concept of a Lyapunov level set. A saturation-dependent Lyapunov function captures real-time information on severity of actuator saturation and leads to less conservative estimation of the DoA for discrete-time systems [10]. It is a good idea to further reduce conservatism in the estimation of DoA using a general Lyapunov function for DOSs . Using the saturation-dependent Lyapunov function , real-time information on severity of saturation thus leads to a less conservative estimation of the DoA , which is based on solution of an LMI optimization problem. Hence, the saturation-dependent Lyapunov function in DOS subject to actuator saturation will get a better result than the one only using quadratic Lyapunov functions , which motivated us for study in this chapter.

References

  1. 10.
    Y. Cao, Z. Lin, Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function. Automatica 37(7), 1235–1241 (2003)MathSciNetCrossRefGoogle Scholar
  2. 12.
    W. Chan, K. Hui, Design of stable actuator saturation compensators in the frequency domain. IEE Proc.-Control Theory Appl. 145(3), 345–352 (1998)CrossRefGoogle Scholar
  3. 74.
    Z. Lin, L. Lv, Set invariance conditions for singular linear systems subject to actuator saturation. IEEE Trans. Automatica Control 52(12), 2351–2355 (2007)MathSciNetCrossRefGoogle Scholar
  4. 143.
    F. Wu, Z. Lin, Q. Zheng, Output feedback stabilization of linear systems with actuator saturation. IEEE Trans. Autom. Control 52(1), 122–128 (2007)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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