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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Robust and non-asymptotic state estimation for MIMO descriptor systems.

Jie Liu1, Da-Yan Liu2, Driss Boutat2

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Summary

This study introduces a novel state estimation framework for descriptor linear systems using auxiliary modulating dynamical systems. The method ensures fixed-time convergence without needing initial conditions or noisy output derivatives.

Keywords:
Descriptor linear system with multi-inputs and multi-outputsRobust and non-asymptotic estimation methodState estimation

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Area of Science:

  • Control Systems Engineering
  • Dynamical Systems Theory
  • Estimation Theory

Background:

  • Descriptor linear systems, particularly those with multiple-input multiple-output (MIMO) configurations, present unique challenges in state estimation due to their inherent algebraic and differential components.
  • Accurate state estimation is crucial for monitoring, control, and fault detection in various engineering applications.

Purpose of the Study:

  • To develop a robust state estimation framework for MIMO descriptor linear systems.
  • To achieve fixed-time, non-asymptotic convergence of state estimates.
  • To minimize sensitivity to noise, especially in discrete-time implementations.

Main Methods:

  • The proposed framework utilizes auxiliary modulating dynamical systems to transform the original descriptor system into a more manageable form.
  • State variables are reconstructed using modulating integrals, circumventing the need for initial conditions.
  • The method avoids the computation of derivatives of potentially noisy outputs in discrete cases.

Main Results:

  • The framework guarantees state estimation convergence within a fixed time, irrespective of initial conditions.
  • The proposed method demonstrates reduced sensitivity to high-frequency noise compared to traditional observers.
  • Numerical simulations validate the effectiveness and practical applicability of the developed state estimation technique.

Conclusions:

  • The auxiliary modulating dynamical systems approach provides an effective solution for state estimation in MIMO descriptor linear systems.
  • The fixed-time convergence and noise robustness make this framework suitable for real-world applications.
  • The study offers valuable insights and a comparative analysis against existing observer methods.