Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Stability01:28

Stability

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.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Multimachine Stability01:25

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Pole and System Stability01:24

Pole and System Stability

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.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Transient and Steady-state Response01:24

Transient and Steady-state Response

In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A uniform LMI formulation for tuning PID, multi-term fractional-order PID, and Tilt-Integral-Derivative (TID) for integer and fractional-order processes.

ISA transactions·2017
Same author

Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

ISA transactions·2011
Same author

Extension of the root-locus method to a certain class of fractional-order systems.

ISA transactions·2008
See all related articles

Related Experiment Video

Updated: Jun 28, 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

An efficient numerical algorithm for stability testing of fractional-delay systems.

Farshad Merrikh-Bayat1, Masoud Karimi-Ghartemani

  • 1Sharif University of Technology, Tehran, Iran.

ISA Transactions
|November 14, 2008
PubMed
Summary

This study introduces a novel numerical algorithm for testing the stability of fractional-delay systems. The method reliably identifies unstable poles, overcoming challenges with complex characteristic functions.

Related Experiment Videos

Last Updated: Jun 28, 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
  • Numerical Analysis
  • Systems Theory

Background:

  • Fractional-delay systems present unique challenges for stability analysis due to their multi-valued characteristic functions on Riemann surfaces.
  • Traditional analytical methods struggle to locate roots of the characteristic equation in the right-half plane of the primary Riemann sheet.
  • The origin as a branch point further complicates stability assessments for these systems.

Purpose of the Study:

  • To develop a robust numerical algorithm for testing the Bounded-Input Bounded-Output (BIBO) stability of fractional-delay systems.
  • To address the limitations of existing analytical techniques for stability analysis of these complex systems.
  • To provide a method that not only determines stability but also identifies the location of unstable poles.

Main Methods:

  • The proposed algorithm leverages Rouche's theorem to determine the number of zeros within a specified contour.
  • It is specifically designed for systems with characteristic functions defined on Riemann surfaces with a finite number of sheets and a branch point at the origin.
  • The numerical approach provides a practical solution for stability testing where analytical methods are insufficient.

Main Results:

  • The algorithm reliably determines the BIBO stability of the considered class of fractional-delay systems.
  • It accurately identifies both the number and the precise location of unstable poles.
  • Validation through several illustrative examples confirms the algorithm's effectiveness and reliability.

Conclusions:

  • The developed numerical algorithm offers a significant advancement for stability analysis of fractional-delay systems.
  • It provides a practical and reliable tool for engineers and researchers working with these complex systems.
  • The method's ability to locate unstable poles enhances its utility beyond simple stability determination.