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Linear time-invariant Systems

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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State Space Representation

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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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Linear Approximation in Frequency Domain

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Related Experiment Video

Updated: May 30, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Robust fault detection for nonlinear networked systems with stochastic interval delay characteristics.

Yong Zhang¹, Zhenxing Liu, Bin Wang

¹School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan, China. zhangyongyq@yahoo.com.cn

ISA Transactions

|August 16, 2011

Summary

This study introduces a new method for robust fault detection in nonlinear networked systems. It effectively balances system robustness with fault sensitivity despite stochastic delays.

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Last Updated: May 30, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Design and Analysis for Fall Detection System Simplification

Design and Analysis for Fall Detection System Simplification

Published on: April 6, 2020

Area of Science:

Control Systems Engineering
Networked Systems Analysis
Nonlinear System Dynamics

Background:

Networked systems introduce complexities like stochastic interval delays, challenging fault detection.
Observer-based robust fault detection (RFD) is crucial for system reliability and safety.
Existing methods struggle to adequately address time-varying delays and uncertainties in nonlinear systems.

Purpose of the Study:

To investigate observer-based robust fault detection (RFD) for nonlinear networked systems with stochastic interval delay.
To formulate RFD as an optimization problem using probabilistic delay information and a performance index.
To design a fault detection filter that achieves a trade-off between robustness and fault sensitivity.

Main Methods:

Utilizing probabilistic distribution of networked-induced time-varying delay.
Formulating RFD as an optimization problem with a proposed performance index.
Constructing the fault detection filter using linear matrix inequalities (LMIs) dependent on delay intervals and occurrence rates.
Applying a two-objective optimization algorithm for sub-optimal trade-offs.

Main Results:

A novel observer-based fault detection filter is designed for nonlinear networked systems.
The filter design explicitly incorporates stochastic interval delay characteristics.
The method achieves a balance between robustness to disturbances/uncertainties and sensitivity to faults.
Numerical simulations validate the effectiveness of the proposed techniques.

Conclusions:

The developed observer-based RFD approach effectively handles stochastic interval delays in nonlinear networked systems.
The proposed optimization framework allows for tuning robustness and fault sensitivity.
The technique offers a promising solution for enhancing the reliability of networked control systems.