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

Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

228
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.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
228
Classification of Systems-II01:31

Classification of Systems-II

140
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
140
Multimachine Stability01:25

Multimachine Stability

151
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:
151
Transient and Steady-state Response01:24

Transient and Steady-state Response

175
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...
175
Second Order systems II01:18

Second Order systems II

101
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.
101
Stability01:28

Stability

101
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...
101

You might also read

Related Articles

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

Sort by
Same author

Multi-state neural dynamics encode antidepressant response: Fusion of resting and task networks.

Brain research bulletin·2026
Same author

A Supervised Contrastive Variational Autoencoder with Probabilistic Latent Alignment for Cross-Domain EEG Emotion Recognition.

Sensors (Basel, Switzerland)·2026
Same author

New results of vehicle sway dynamic system via a new LKF lemma and optimization algorithm.

ISA transactions·2026
Same author

CV-EEGNet: A Compact Complex-Valued Convolutional Network for End-to-End EEG-Based Emotion Recognition.

Sensors (Basel, Switzerland)·2026
Same author

Adaptive Hierarchical Event-Triggered H<sub>∞</sub> Output Tracking of IT2 Fuzzy Heterogeneous Multiagent Systems Under Multiple-Channel DoS Attacks.

IEEE transactions on cybernetics·2026
Same author

Disease-specific network pattern of perinatal depression revealed by Common Orthogonal Basis Extraction.

Brain research bulletin·2026

Related Experiment Video

Updated: Jun 24, 2025

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

10.3K

Parametric Stability Criteria for Delayed Recurrent Neural Networks via Flexible Delay-Dividing Method.

Yapeng Liu, Kun Zhou, Shouming Zhong

    IEEE Transactions on Neural Networks and Learning Systems
    |June 12, 2024
    PubMed
    Summary

    This study enhances recurrent neural network (RNN) stability analysis for systems with time-varying delays (TVDs). A novel delay-dividing method improves stability criteria, validated through simulations.

    More Related Videos

    Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments
    05:19

    Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments

    Published on: November 12, 2019

    7.0K
    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
    12:03

    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

    Published on: May 25, 2019

    8.4K

    Related Experiment Videos

    Last Updated: Jun 24, 2025

    Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
    11:18

    Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

    Published on: March 2, 2015

    10.3K
    Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments
    05:19

    Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments

    Published on: November 12, 2019

    7.0K
    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
    12:03

    A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

    Published on: May 25, 2019

    8.4K

    Area of Science:

    • Control Theory
    • Artificial Intelligence
    • Dynamical Systems

    Background:

    • Recurrent Neural Networks (RNNs) are crucial for sequential data processing.
    • Stability analysis of RNNs with time-varying delays (TVDs) presents significant challenges.
    • Existing methods often lack flexibility in handling complex delay intervals.

    Purpose of the Study:

    • To investigate and improve the stability criteria for RNNs with interval TVDs.
    • To introduce a flexible delay-dividing method for enhanced stability analysis.
    • To develop novel techniques for managing integral terms in stability analysis.

    Main Methods:

    • A flexible delay-dividing method is proposed, partitioning delay intervals using linear combinations.
    • A parameter-dependent Lyapunov-Krasovskii functional (LKF) is constructed.
    • A novel linear technique is employed to eliminate integral terms in LKF derivatives.

    Main Results:

    • The proposed method effectively handles interval time-varying delays in RNNs.
    • New stability criteria are derived, offering improved performance over existing approaches.
    • Simulation examples demonstrate the validity and advantages of the developed criteria.

    Conclusions:

    • The flexible delay-dividing method provides a robust framework for RNN stability analysis with TVDs.
    • The novel approach offers enhanced stability criteria, crucial for reliable RNN applications.
    • This research contributes to the theoretical understanding and practical implementation of stable RNNs.