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Improved delay-range-dependent stability analysis of a time-delay system with norm bounded uncertainty.

Rajeeb Dey1, Sandip Ghosh2, Goshaidas Ray3

  • 1Department of Electrical Engineering, National Institute of Technology, Silchar 788010, India.

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|July 21, 2015
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Summary

This study enhances stability analysis for uncertain linear time-delay systems using integral inequalities. It compares non-delay partitioning and delay partitioning methods for improved robustness and delay bounds.

Keywords:
Linear matrix inequality (LMI)Lyapunov–Krasovskii (LK) functionalRobust stabilityTime-delay systems (TDS)

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Area of Science:

  • Control Theory
  • Systems Engineering
  • Applied Mathematics

Background:

  • Linear time-delay systems are crucial in various engineering fields.
  • Robust stability analysis is essential for system reliability under uncertainty.
  • Existing methods for delay-range-dependent stability analysis have limitations.

Purpose of the Study:

  • To develop improved robust delay-range-dependent stability criteria for uncertain linear time-delay systems.
  • To compare the efficacy of non-delay partitioning (NDP) and delay partitioning (DP) approaches.
  • To investigate the trade-offs between delay bounds and computational complexity.

Main Methods:

  • Utilizing integral inequalities to approximate uncertain integration limits in Lyapunov-Krasovskii functionals.
  • Applying both non-delay partitioning (NDP) and delay partitioning (DP) frameworks.
  • Comparative analysis of the derived stability criteria.

Main Results:

  • The proposed integral inequality approach yields less conservative stability results compared to existing methods.
  • A detailed comparison highlights the relative merits of NDP and DP.
  • Identified trade-offs allow for optimizing delay bounds and reducing decision variables.

Conclusions:

  • The improved stability analysis provides more accurate and less conservative results for uncertain linear time-delay systems.
  • The comparative study offers valuable insights for selecting appropriate analysis methods.
  • Numerical examples validate the effectiveness and applicability of the proposed approach.