Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Linear time-invariant Systems

Linear time-invariant Systems

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...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

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....

Linear Approximation in Time Domain

Linear Approximation in Time Domain

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,...

Second Order systems II

Second Order systems II

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.

Classification of Systems-I

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

BIBO stability of continuous and discrete -time systems

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

Reprogramming the spleen-brain axis: Splenic monocyte/macrophage-mediated nanotherapy for ischemic stroke.

Acta pharmaceutica Sinica. B·2026

Same author

A Collaborative Neurodynamic Approach to Sharpness-Aware Minimization for Improving Generalization of Deep Learning.

IEEE transactions on cybernetics·2026

Same author

Enhancing interpretable soft sensing with embedded hybrid modeling: the GraphTrans approach for industrial processes.

ISA transactions·2026

Same author

Endometrial Cancer of the Uterine Isthmus: A Cohort Study on Clinicopathological Features and Prognosis.

Cancer medicine·2026

Same author

Dietary Fermented Chinese Chive Juice Improves Growth Performance and Reshapes the Fresh Meat Volatile Flavor Profile of Small-Tailed Han Sheep.

Animals : an open access journal from MDPI·2026

Same author

Distribution of divalent small interfering RNA into neurons of sensory ganglia produces selective, durable knockdown of Nav1.7 and strong analgesia.

Pain·2026

Search research articles

Related Experiment Video

Updated: Jul 19, 2025

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

A robust sparse identification method for nonlinear dynamic systems affected by non-stationary noise.

Zhihang Hao¹, Chunhua Yang¹, Keke Huang¹

¹School of Automation, Central South University, Changsha 410083, China.

Chaos (Woodbury, N.Y.)

|August 7, 2023

Summary

This study introduces a novel method for identifying nonlinear dynamics from noisy data. The proposed approach enhances accuracy by robustly handling non-stationary noise, improving sparse identification results.

More Related Videos

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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

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

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

Published on: May 25, 2019

Related Experiment Videos

Last Updated: Jul 19, 2025

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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

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

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

Published on: May 25, 2019

Area of Science:

Science and Engineering
Dynamical Systems Theory
Data-driven Modeling

Background:

Identifying nonlinear system dynamics from data is crucial but challenging.
Noisy data, especially non-stationary noise, significantly degrades the accuracy of traditional identification methods.
Existing techniques often fail to adequately address the impact of non-stationary noise on system identification.

Purpose of the Study:

To develop a robust method for identifying nonlinear dynamics from data contaminated by non-stationary noise.
To improve the accuracy and reliability of sparse identification of dynamics in the presence of noise.
To propose a novel mathematical framework that quantitatively accounts for non-stationary noise.

Main Methods:

Proposed a weighted ℓ1-regularized and insensitive loss function for robust sparse identification.
Formulated the robust identification problem using a sparse identification mathematical model.
Developed an efficient optimization algorithm using smooth approximation and the alternating direction multiplier method.
Utilized a novel weighted ℓ1-regularized and insensitive loss function to mitigate non-stationary noise effects.

Main Results:

The proposed method effectively mitigates the adverse effects of non-stationary noise.
Achieved enhanced sparsity of results compared to traditional loss functions.
Demonstrated superior identification accuracy in extensive experiments on various nonlinear dynamical systems.
Outperformed state-of-the-art methods in robust identification tasks.

Conclusions:

The developed weighted ℓ1-regularized and insensitive loss function-based sparse identification method offers improved accuracy and robustness.
The approach provides a reliable solution for identifying nonlinear dynamics from noisy datasets.
This work advances the field of data-driven system identification by effectively handling non-stationary noise.