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Stability of Lurie Time-Varying Systems with Time-Varying Delay Feedbacks

  • Shuli Guo
  • Lina Han
Chapter

Abstract

In this chapter, the stability problems of Lurie nonlinear system with time-varying plant and time-varying actuator under time-varying delay feedback are presented. First, absolute stability criteria, which we define as solvable matrix inequalities, are outlined by constructing a Lyapunov–Razumikhn functional. Second, we analyze these solvable matrix inequalities, and give their sufficient and necessary solvable conditions that are easily computed in practical systems. Third, based on our norm definition, solvable conditions and time-delay bound estimations can be obtained from two cases of solvable norm inequalities. More importantly, by analyzing all obtained procedures, we present the optimal combination method about a pair of \((\tau ,Q)\). Finally, an interested numerical example is presented to illustrate the above results effectively.

Notes

Acknowledgements

This work is Supported by National Key Research and Development Program of China (2017YFF0207400).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Key Laboratory of Complex System Intelligent Control and Decision, School of AutomationBeijing Institute of TechnologyBeijingChina
  2. 2.Department of Cardiovascular Internal Medicine of Nanlou Branch, National Clinical Research Center for Geriatric DiseasesChinese PLA General HospitalBeijingChina

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