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Dissipativity analysis for discrete singular systems with time-varying delay.

Zhiguang Feng1, Wenxing Li2, James Lam3

  • 1The College of Automation, Harbin Engineering University, Harbin 150001, China.

ISA Transactions
|May 31, 2016
PubMed
Summary

This study analyzes dissipativity for discrete singular systems with time-varying delays. New methods ensure system admissibility and dissipativity, enhancing control system stability and performance analysis.

Keywords:
Discrete-time systemDissipativitySingular systemTime-varying delay

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Area of Science:

  • Control Theory
  • Systems Engineering
  • Nonlinear Dynamics

Background:

  • Discrete singular systems are crucial in advanced control applications.
  • Time-varying delays introduce significant challenges in system analysis and stability.
  • Dissipativity analysis is fundamental for guaranteeing system stability and performance.

Purpose of the Study:

  • To investigate the dissipativity analysis for discrete singular systems with time-varying delays.
  • To develop less conservative criteria for system admissibility and dissipativity.
  • To extend the analysis to include H∞ performance and passivity.

Main Methods:

  • Utilizing a novel inequality that improves upon the Jensen inequality.
  • Employing an enhanced reciprocally convex combination approach.
  • Applying these methods to derive sufficient conditions for system properties.

Main Results:

  • Sufficient criteria for guaranteeing the admissibility and dissipativity of discrete singular systems with time-varying delays were established.
  • The proposed criteria are shown to be less conservative than existing methods.
  • H∞ performance characterization and passivity analysis were successfully performed.

Conclusions:

  • The developed methods provide effective tools for analyzing discrete singular systems with time-varying delays.
  • The criteria enhance the robustness and stability guarantees for these complex systems.
  • Numerical examples validate the proposed approach's efficacy and superiority.