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Refined Wirtinger-type integral inequality.

Liansheng Zhang1,2, Shuxia Wang1

  • 11Department of Mathematics and Physics, Beijing Institute of Petro-Chemical Technology, Beijing, China.

Journal of Inequalities and Applications
|May 18, 2018
PubMed
Summary

This study introduces a novel Wirtinger-type double integral inequality, enhancing stability analysis for delayed control systems. The refined inequality offers less conservative results compared to existing methods.

Keywords:
Stability analysisSystems with time-delaysWirtinger-type double integral inequality

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Area of Science:

  • Mathematical Analysis
  • Control Theory

Background:

  • Integral inequalities are crucial for analyzing control systems.
  • Existing Wirtinger-based inequalities have limitations in conservatism.

Purpose of the Study:

  • To establish a new class of Wirtinger-type double integral inequalities.
  • To refine existing inequalities for reduced conservatism.

Main Methods:

  • Derivation based on extreme value conditions of multivariable functions.
  • Generalization and refinement of classical Wirtinger-type inequalities.

Main Results:

  • A novel Wirtinger-type double integral inequality is established.
  • The proposed inequality demonstrates reduced conservatism compared to Jensen's and other existing inequalities.

Conclusions:

  • The refined inequality provides less conservative stability criteria for delayed control systems.
  • This advancement offers improved analytical tools in control theory.