A Lifting Technique for Sampling Periods

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


Using traditional methods on LMIs , an invariant set Ω(P, ρ) as the DoA has been obtained in [52]. All trajectories of a control system are kept inside the DoA at every step [163]. An important issue of the works in previous chapters is how to design a proper controller and how to estimate the DoA for DOSs with actuator saturation . Note that invariant ellipsoids are also used to estimate the DoA of DOSs [45]. In [19], researches on the DoA have been given for uncertain polynomial continuous-time systems . Moreover, a central idea of existing methodologies on estimating the DoA is to use a contractively invariant set associated to proper Lyapunov functions , such as Lyapunov functions with ellipsoidal estimates, polyhedral Lyapunov functions , and piecewise quadratic Lyapunov functions . Although these problems have been examined extensively from various aspects recently, estimating and enlarging the DoA is still a difficult task.


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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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