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Further results on delay-range-dependent stability with additive time-varying delay systems.

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  • 1Department of Automation Engineering Institute of Mechatronoptic System, Chienkuo Technology University, 1 Chien-Shous N. Load, Changhua 500, Taiwan, ROC.

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Summary

This study introduces novel conditions for stability analysis of time-varying delay systems. New methods reduce conservatism in stability criteria for network-based control systems.

Keywords:
Additive time-varying componentsDelay-range-dependentIntegral inequality approachLinear matrix inequalityTime-varying delay

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Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Time-varying delay systems are prevalent in network-based control systems.
  • Stability analysis of these systems is crucial for reliable operation.
  • Existing methods can be conservative, limiting the analysis of delays.

Purpose of the Study:

  • To develop new delay-range-dependent stability conditions for time-varying delay systems.
  • To propose a less conservative stability analysis framework.
  • To enhance the analysis of systems with multiple time-varying delays.

Main Methods:

  • Utilizing a Lyapunov-Krasovskii framework.
  • Employing an integral inequality approach (IIA) for Leibniz-Newton formula terms.
  • Constructing a novel Lyapunov-Krasovskii functional incorporating delay range information.
  • Formulating criteria using linear matrix inequality (LMI).

Main Results:

  • A new, less conservative delay-range-dependent stability criterion is established.
  • The proposed method is effective for systems with two additive time-variant delays.
  • Numerical examples demonstrate reduced conservatism and improved maximal allowable delay.

Conclusions:

  • The developed criteria offer a simpler and less conservative approach to stability analysis.
  • The methods are applicable to a general class of delay systems, particularly in network-based control.
  • The findings contribute to more robust and reliable control system design.