Stability Analysis of High Frequency NCSs

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 430)


For the reason of that high frequency sampling will increase the possibility of network congestion, high frequency constricts of NCSs is more affected by time delays and packets dropout than low frequency constricts. Therefore, designing a high frequency system to describe NCSs and satisfying stability performance by using delta operator approach is a key task in this topic. To deal with finite frequency requirements, both weighting functions and frequency gridding has been utilized in [150] and [286], respectively. KYP lemma establishes equivalence between such frequency domain inequality for a transfer function and a LMI for its state space realization [198]. It originates from Popov’s criterion [191]. The Popov’s frequency condition is equivalent to existence of a certain simple Lyapunov function form [133, 282]. Based on the famous Shannon sampling theory, sampling frequency is much larger than system frequency. Goodwin introduced delta operator method to deal with high frequency sampling in [82]. A number of results on delta operator method have been reported in literatures, such as [215, 285, 284]. The generalized KYP lemma in Chapter 9 has given a direct treatment of the finite frequency performance, thus it is can avoid computational burden and guarantee gain property performances simultaneously as in [115, 118, 119].


Inverted Pendulum Feedback Channel Packet Dropout High Frequency Sampling Delta Operator 
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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2012

Authors and Affiliations

  • Hongjiu Yang
    • 1
  • Yuanqing Xia
    • 2
  • Peng Shi
    • 3
  • Ling Zhao
    • 4
  1. 1.Institute of Electrical EngineeringYanshan UniversityQinhuangdaoChina, People’s Republic
  2. 2.School of AutomationBeijing Institute of TechnologyBeijingChina, People’s Republic
  3. 3.Department of Computing and Mathematical SciencesUniversity of GlamorganPontypriddUnited Kingdom
  4. 4.College of Mechanical EngineeringYanshan UniversityQinhuangdaoChina, People’s Republic

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