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Stability analysis for linear switched systems with time-varying delay.

Xi-Ming Sun1, Wei Wang, Guo-Ping Liu

  • 1Research Center of Information and Control, Dalian University of Technology, Dalian. LiaoNing, China. sunxm@dlut.edu.cn

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|March 20, 2008
PubMed
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This study addresses stability in linear switched systems with time-varying delays. A new method using linear matrix inequalities (LMIs) guarantees system stability even with unknown delay derivatives.

Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Linear switched systems are crucial in modern control.
  • Time-varying delays introduce significant stability challenges.
  • Existing stability criteria for delayed systems can be conservative.

Purpose of the Study:

  • To investigate the stability of linear switched systems with time-varying delays.
  • To develop a less conservative stability criterion.
  • To provide a method for easily obtaining delay bounds for stability.

Main Methods:

  • Analysis of Hurwitz convex combination for stability.
  • Utilizing linear matrix inequalities (LMIs) for stability analysis.
  • Derivation of conditions for systems with unknown constant delay derivatives.

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Main Results:

  • Stability is guaranteed for linear switched systems with time-varying delays under a specific delay bound.
  • The proposed method provides a less conservative stability criterion compared to existing ones, especially for constant delays.
  • Delay bounds ensuring system stability are readily computable via LMIs.

Conclusions:

  • The developed stability criteria are effective for linear switched systems with time-varying delays.
  • The proposed approach offers improved performance over existing methods.
  • Simulation results validate the efficacy of the stability analysis technique.