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New stabilization for dynamical system with two additive time-varying delays.

Lianglin Xiong1, Fan Yang1, Xiaozhou Chen1

  • 1School of Mathematics and Computer Science, Yunnan University of Nationalities, Kunming 650500, China.

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Summary
This summary is machine-generated.

This study introduces a new stabilization criterion for systems with time-varying delays. The method improves stability analysis by reducing conservatism and enhancing effectiveness.

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Area of Science:

  • Control Systems Engineering
  • Applied Mathematics

Background:

  • Time-varying delays are common in dynamical systems, posing challenges for stability analysis.
  • Existing stabilization criteria can be overly conservative, limiting their practical application.

Purpose of the Study:

  • To develop a novel delay-dependent stabilization criterion for systems with two additive time-varying delays.
  • To improve the conservatism and effectiveness of stability analysis for such systems.

Main Methods:

  • Construction of a novel Lyapunov functional.
  • Application of the delay decomposition technique.
  • Utilization of the reciprocally convex approach.

Main Results:

  • A tighter upper bound for the derivative of the Lyapunov functional was obtained.
  • The proposed criterion demonstrates reduced conservatism compared to existing methods.
  • Effectiveness was validated through two illustrative examples.

Conclusions:

  • The new delay-dependent stabilization criterion offers a less conservative and more effective approach.
  • The combination of delay decomposition and reciprocally convex methods is advantageous for stability analysis.