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Partial state estimation for linear systems with output and input time delays.

Q P Ha1, Nguyen D That2, Phan T Nam3

  • 1Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW 2007, Australia.

ISA Transactions
|January 18, 2014
PubMed
Summary
This summary is machine-generated.

This study presents a new method for designing partial state observers for linear systems with time delays in both output and control inputs. The approach ensures exponential convergence of observer errors, enhancing system stability analysis.

Keywords:
Delay decompositionLyapunov–Krasovskii functionalOutput and input delayPartial state observerε-Convergence

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Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Linear systems are fundamental in control engineering.
  • Time delays in system measurements and control inputs pose significant challenges in observer design.
  • Partial state observers are crucial for estimating unmeasured states in complex systems.

Purpose of the Study:

  • To develop a novel method for designing minimal-order partial state observers for linear systems with time delays.
  • To guarantee exponential convergence of observer errors for enhanced system performance.
  • To provide constructive design algorithms and validate their effectiveness through numerical examples.

Main Methods:

  • Utilizing augmented Lyapunov-Krasovskii functionals with triple-integral terms.
  • Incorporating information from both delayed output and control input.
  • Deriving existence conditions using matrix inequalities.

Main Results:

  • A novel approach for minimal-order observer design is proposed.
  • Guaranteed ε-convergence with an exponential rate for observer errors.
  • Existence conditions established for systems with output and input delays, and output-only delays.

Conclusions:

  • The proposed observer design method is effective for linear systems with time delays.
  • The method ensures robust observer error convergence, crucial for system monitoring and control.
  • Numerical examples confirm the practicality and effectiveness of the developed design algorithms.