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

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

1.1K
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....
1.1K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.4K
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...
1.4K
Linear time-invariant Systems01:23

Linear time-invariant Systems

1.1K
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...
1.1K
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

1.9K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.9K
Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

496
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
496
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

459
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,...
459

You might also read

Related Articles

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

Sort by
Same author

Improved results on delay-interval-dependent robust stability criteria for uncertain neutral-type systems with time-varying delays.

ISA transactions·2016
Same author

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type.

ISA transactions·2015
Same author

Further improvement on delay-range-dependent robust absolute stability for Lur'e uncertain systems with interval time-varying delays.

ISA transactions·2015
Same author

New results on delay-range-dependent stability analysis for interval time-varying delay systems with non-linear perturbations.

ISA transactions·2015
Same author

Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays.

ISA transactions·2014
Same author

Further results on delay-range-dependent stability with additive time-varying delay systems.

ISA transactions·2013

Related Experiment Video

Updated: Apr 22, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

703

Improved delay-range-dependent robust stability for uncertain systems with interval time-varying delay.

Pin-Lin Liu1

  • 1Department of Automation Engineering Institute of Mechatronoptic System, Chienkuo Technology University, Changhua 500, Taiwan, ROC.

ISA Transactions
|October 9, 2014
PubMed
Summary

This study introduces novel stability criteria for linear systems with time-varying delays and uncertainties. The new methods offer less conservative results, improving stability analysis for complex systems.

Keywords:
Delay-range-dependentDelayed decomposition approach (DDA)Integral inequality approach (IIA)Interval time-varying delayLinear matrix inequality (LMI)

Related Experiment Videos

Last Updated: Apr 22, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

703

Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Linear systems with time-varying delays present significant stability challenges.
  • Norm-bounded uncertainties further complicate stability analysis.
  • Existing stability criteria often exhibit conservatism, limiting their applicability.

Purpose of the Study:

  • To develop improved delay-range-dependent stability and robust stability criteria.
  • To reduce conservatism in stability analysis for linear systems with time-varying delays.
  • To enhance the maximum admissible upper bound (MAUB) for time delays.

Main Methods:

  • Utilizing a Lyapunov-Krasovskii functional (LKF) incorporating delay bounds.
  • Applying the delayed decomposition approach (DDA).
  • Theoretically establishing new criteria with fewer matrix variables.

Main Results:

  • Derived novel stability criteria that are less conservative than previous methods.
  • Demonstrated improved performance in overcoming MAUB limitations for time delays.
  • Validated the effectiveness through four well-known examples.

Conclusions:

  • The proposed stability criteria offer significant improvements in reducing conservatism.
  • The new approach enhances the analysis of linear systems with time-varying delays and uncertainties.
  • This work provides a less conservative and more effective framework for stability analysis.