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Linear systems with unstructured multiplicative uncertainty: Modeling and robust stability analysis.

Radek Matušů1, Bilal Şenol2, Celaleddin Yeroğlu2

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Summary
This summary is machine-generated.

This study presents a method for creating uncertain models of Linear Time-Invariant (LTI) systems with multiplicative uncertainty. It demonstrates robust stability analysis for these models in control system design.

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Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Robust Control

Background:

  • Linear Time-Invariant (LTI) systems are fundamental in control engineering.
  • Unstructured multiplicative uncertainty poses challenges in system modeling and analysis.
  • Robust stability is crucial for reliable control system performance.

Purpose of the Study:

  • To develop an approach for constructing uncertain models of continuous-time LTI SISO systems.
  • To apply robust stability investigation techniques to these uncertain models.
  • To illustrate the methodology with practical examples of different order plants.

Main Methods:

  • Modeling systems with unstructured multiplicative uncertainty using a nominal system and weight function.
  • Employing robust stability criteria for analysis.
  • Utilizing illustrative examples including first, second, and third-order plants with parametric uncertainty.

Main Results:

  • Successful construction of uncertain models for various plant orders.
  • Demonstration of robust stability analysis for feedback loops with uncertain models.
  • Discussion of the obtained results and their implications for controller design.

Conclusions:

  • The proposed approach provides a systematic way to model and analyze uncertain LTI systems.
  • Robust stability can be effectively investigated for systems with unstructured multiplicative uncertainty.
  • The methodology is validated through practical examples, offering insights for control design.