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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

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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...
471
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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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,...
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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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....
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First Order Systems01:21

First Order Systems

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First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
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Second Order systems II01:18

Second Order systems II

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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.
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Updated: Sep 24, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Interval estimation for nabla fractional order linear time-invariant systems.

Yingdong Wei1, Yiheng Wei2, Yong Wang3

  • 1Department of Automation, University of Science and Technology of China, 230026 Hefei, Anhui, China; Department of Advanced Design and Systems Engineering, City University of Hong Kong, Hong Kong.

ISA Transactions
|May 10, 2022
PubMed
Summary

This study introduces a framework for interval estimation in fractional-order linear time-invariant (LTI) systems with uncertainties. It develops interval observers ensuring stable and positive error dynamics for enhanced system analysis.

Keywords:
Coordinate transformationInterval estimationNabla fractional order LTI systemsPositive systems theory

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Area of Science:

  • Control Theory
  • Fractional Calculus
  • Systems Engineering

Background:

  • Fractional-order systems are increasingly used in modeling complex phenomena.
  • Interval estimation is crucial for systems with bounded uncertainties.
  • Existing methods may not fully address stability and positivity in fractional systems.

Purpose of the Study:

  • To develop a framework for interval estimation in nabla Caputo fractional-order LTI systems.
  • To design interval observers that guarantee stable and positive error dynamics.
  • To extend the applicability of interval estimation to a broader class of fractional systems.

Main Methods:

  • Utilizing fractional-order positive systems theory for observer design.
  • Deriving systematic conditions for stability and positivity.
  • Applying Luenberger-type observer structures and coordinate transformation techniques.

Main Results:

  • A framework for interval estimation in fractional-order LTI systems with bounded uncertainties is established.
  • Novel interval observers ensuring stable and positive error dynamics are designed.
  • The proposed methods are validated through simulations in fault detection and fractional-order circuit scenarios.

Conclusions:

  • The developed framework effectively achieves interval estimation for fractional-order LTI systems.
  • The designed interval observers are practical and useful for applications like fault detection.
  • The coordinate transformation technique enhances the generality of interval observer design.