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

State Space Representation01:27

State Space Representation

237
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
237
Linear time-invariant Systems01:23

Linear time-invariant Systems

289
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...
289
State Space to Transfer Function01:21

State Space to Transfer Function

236
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
236
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

667
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
667
Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

2.8K
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
2.8K
Transfer Function to State Space01:23

Transfer Function to State Space

297
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
297

You might also read

Related Articles

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

Sort by
Same journal

Analysis of strength degradation of coal and rock masses and stability of mined areas under long term immersion environment.

PloS one·2026
Same journal

Biogenic Silver-Selenium nanocomposite with anticancer activity and potent efficacy against vancomycin-resistant Staphylococcus aureus.

PloS one·2026
Same journal

Preparation and physicochemical characterization of a biodegradable chitosan/carboxymethyl cellulose hydrogel synthesized in NaOH/urea medium.

PloS one·2026
Same journal

Action-guilt, survivor-guilt, and depression in combat-related PTSD.

PloS one·2026
Same journal

Explainable machine learning for predicting activities of daily living at discharge in stroke patients: A retrospective study using SHAP interpretability.

PloS one·2026
Same journal

Deep learning based two-way feature depiction model for brain tumor detection.

PloS one·2026
See all related articles

Related Experiment Video

Updated: Jul 19, 2025

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

13.6K

Space-time POD and the Hankel matrix.

Peter Frame1, Aaron Towne1

  • 1Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, United States of America.

Plos One
|August 10, 2023
PubMed
Summary
This summary is machine-generated.

Time-delay embedding and singular value decomposition (SVD) approximate space-time proper orthogonal decomposition (POD) modes for reduced-order modeling. This reveals insights into Hankel modes and improves POD accuracy and computation.

More Related Videos

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

12.7K
2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

10.1K

Related Experiment Videos

Last Updated: Jul 19, 2025

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

13.6K
MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
09:46

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions

Published on: May 10, 2012

12.7K
2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

10.1K

Area of Science:

  • Dynamical Systems and Control Theory
  • Data-Driven Modeling
  • Scientific Computing

Background:

  • Time-delay embedding is a foundational technique for data-driven reduced-order modeling.
  • Singular value decomposition (SVD) of block Hankel matrices is central to popular reduced-order modeling methods.
  • Understanding the theoretical underpinnings of Hankel modes is crucial for advancing these methods.

Purpose of the Study:

  • To establish a theoretical connection between Hankel modes derived from time-delay embedding and space-time proper orthogonal decomposition (POD) modes.
  • To provide a clear interpretation of Hankel modes by relating them to classical POD theory.
  • To identify opportunities for improving the accuracy and computational efficiency of reduced-order models.

Main Methods:

  • Formulation of a block Hankel matrix from successive delay embeddings of a dynamical system's state.
  • Application of singular value decomposition (SVD) to the block Hankel matrix.
  • Analysis of the left singular vectors and singular values in relation to space-time POD modes and energies.
  • Investigation using the correlation matrix derived from the Hankel matrix.

Main Results:

  • Left singular vectors of the Hankel matrix are discrete approximations of space-time POD modes.
  • Singular values correspond to the square roots of POD energies.
  • Insights into Hankel mode interpretation, including the meaning of rows/columns, optimal norms, time-step impact, and embedding dimension effects.
  • Demonstration that standard space-only POD and spectral POD are limiting cases of this framework.

Conclusions:

  • The study provides a rigorous theoretical link between SVD of Hankel matrices and space-time POD.
  • This connection enhances the interpretability and theoretical grounding of data-driven reduced-order modeling techniques.
  • The established relationships offer pathways to improve computational efficiency and accuracy in practical applications.