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Related Concept Videos

State Space Representation01:27

State Space Representation

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.
Consider an RLC circuit, a...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Feedback control systems01:26

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear time-invariant Systems01:23

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.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...

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Related Experiment Video

Updated: Jun 21, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

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

Set-membership fuzzy filtering for nonlinear discrete-time systems.

Fuwen Yang1, Yongmin Li

  • 1School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China. fwyang@ecust.edu.cn

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|July 25, 2009
PubMed
Summary

This study introduces a new nonlinear set-membership filtering (SMF) method for discrete-time systems using Takagi-Sugeno fuzzy models. The approach provides a guaranteed state estimation ellipsoid, improving accuracy for nonlinear systems.

Related Experiment Videos

Last Updated: Jun 21, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

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

Area of Science:

  • Control Systems Engineering
  • Nonlinear System Analysis
  • Fuzzy Logic Systems

Background:

  • Set-membership filtering (SMF) addresses state estimation for systems with bounded uncertainties.
  • Traditional methods often linearize nonlinear systems around a single point, limiting accuracy.
  • Approximating nonlinear systems over a set of states is challenging.

Purpose of the Study:

  • To develop a novel nonlinear SMF method for discrete-time systems.
  • To utilize Takagi-Sugeno (T-S) fuzzy models for improved nonlinear system approximation.
  • To determine a state estimation ellipsoid encompassing true states despite bounded noises and modeling errors.

Main Methods:

  • Employing Takagi-Sugeno (T-S) fuzzy models to represent discrete-time nonlinear systems.
  • Applying the S-procedure technique for robust state estimation within the set-membership framework.
  • Developing a recursive algorithm to compute a state estimation ellipsoid.

Main Results:

  • A new nonlinear SMF estimation method is proposed for discrete-time systems.
  • The method generates a state estimation ellipsoid guaranteed to contain the true system state.
  • A recursive algorithm efficiently computes the smallest possible estimate set by solving semidefinite programming problems.

Conclusions:

  • The proposed fuzzy-based SMF method effectively estimates states for discrete-time nonlinear systems.
  • The technique handles unknown-but-bounded process and measurement noises robustly.
  • The approach offers improved accuracy over point-based linearization methods in SMF.