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Sampled-data control for linear time-delay distributed parameter systems.

Zi-Peng Wang1, Huai-Ning Wu2, Xiao-Hong Wang1

  • 1School of Electrical Engineering, University of Jinan, Jinan 250022, China.

ISA Transactions
|March 4, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces sampled-data control (SDC) for time-delay distributed parameter systems (DPSs). The new method uses spatial linear matrix inequalities (LMIs) to stabilize these complex systems effectively.

Keywords:
Distributed parameter systems (DPS)Sampled-data controlSpatial linear matrix inequalityTime-varying delay

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Area of Science:

  • Control Engineering
  • Applied Mathematics
  • Systems Theory

Background:

  • Real-world systems often exhibit spatiotemporal dynamics, presenting challenges as time-delay distributed parameter systems (DPSs).
  • The presence of time-delay in DPSs can lead to system instability, complicating analysis and design.
  • Existing research on sampled-data control (SDC) for time-delay DPSs is limited.

Purpose of the Study:

  • To develop a novel sampled-data control (SDC) strategy for linear time-delay DPSs.
  • To address the complexities introduced by time-delays in parabolic partial differential equations (PDEs).
  • To leverage digital control technologies for stabilizing DPSs with time-delays.

Main Methods:

  • A sampled-data control (SDC) design is formulated using spatial linear matrix inequalities (LMIs).
  • An appropriate Lyapunov functional is constructed to ensure exponential stability.
  • The stabilization conditions are designed to accommodate both slow and fast-varying time delays.

Main Results:

  • The proposed SDC method successfully stabilizes linear time-delay DPSs described by parabolic PDEs.
  • The developed Lyapunov functional provides a robust condition for exponential stabilization.
  • Simulation results confirm the effectiveness of the LMI-based control design.

Conclusions:

  • The study presents a viable SDC approach for stabilizing complex time-delay DPSs.
  • The method offers a theoretical and practical advancement in control engineering for systems with delays.
  • The findings are applicable to a range of dynamic systems affected by time-varying delays.