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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.
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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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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.
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The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
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Quantifying the robustness of a chaotic system.

J C Sprott1

  • 1Physics Department, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA.

Chaos (Woodbury, N.Y.)
|April 2, 2022
PubMed
Summary

This study introduces a method to measure the robustness of chaotic systems. It quantifies how much system parameters can change before chaos is likely destroyed, aiding in understanding system stability.

Area of Science:

  • * Nonlinear Dynamics and Chaos Theory
  • * Computational Physics and Mathematics

Background:

  • * Chaotic systems exhibit sensitive dependence on initial conditions.
  • * Quantifying the robustness of chaos is crucial for practical applications and theoretical understanding.
  • * Existing methods may not fully capture the parameter space's influence on chaotic behavior.

Purpose of the Study:

  • * To propose a novel scheme for quantifying the robustness of chaotic systems.
  • * To determine the parameter alteration threshold at which chaos destruction probability exceeds 50%.
  • * To assess the robustness of common dissipative chaotic systems.

Main Methods:

  • * Development of a quantitative scheme based on parameter perturbation.
  • * Application of the Monte Carlo method for probabilistic assessment.

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  • * Testing on diverse dissipative chaotic maps and flows.

    • Main Results:

    • * The proposed scheme successfully quantifies chaos robustness across different systems.
    • * Identified specific parameter ranges that maintain chaotic behavior.
    • * Demonstrated variability in robustness based on system complexity and parameter count.

    Conclusions:

    • * The developed method provides a robust metric for chaotic system stability.
    • * Findings offer insights into the parameter sensitivity of chaotic dynamics.
    • * This quantification aids in designing and controlling chaotic systems.