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Related Concept Videos

State Space Representation01:27

State Space Representation

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...
Transfer Function in Control Systems01:21

Transfer Function in Control Systems

The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
State Space to Transfer Function01:21

State Space to Transfer Function

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:
Linear time-invariant Systems01:23

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 calculated...
Convolution Properties I01:20

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
Transfer Function to State Space01:23

Transfer Function to State Space

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 RLC...

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Related Experiment Video

Updated: Jul 6, 2026

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature
09:39

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

Published on: November 18, 2019

Local information transfer as a spatiotemporal filter for complex systems.

Joseph T Lizier1, Mikhail Prokopenko, Albert Y Zomaya

  • 1CSIRO Information and Communications Technology Centre, Locked Bag 17, North Ryde, NSW 1670, Australia. jlizier@it.usyd.edu.au

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary
This summary is machine-generated.

We introduce local transfer entropy to map information flow in complex systems. This method reveals that particles like gliders are key information carriers in cellular automata.

Related Experiment Videos

Last Updated: Jul 6, 2026

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature
09:39

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

Published on: November 18, 2019

Area of Science:

  • Complex Systems Science
  • Information Theory
  • Computational Science

Background:

  • Information transfer is crucial for understanding complex systems.
  • Existing measures like transfer entropy provide averaged insights.
  • Spatiotemporal dynamics of information flow remain underexplored.

Purpose of the Study:

  • To develop a novel measure of local information transfer.
  • To analyze spatiotemporal information flow profiles in complex systems.
  • To investigate the role of emergent structures in information transfer.

Main Methods:

  • Derivation of local transfer entropy from averaged transfer entropy.
  • Application of local transfer entropy to cellular automata models.
  • Analysis of spatiotemporal profiles to identify information transfer agents.

Main Results:

  • Local transfer entropy effectively profiles information flow into spatiotemporal points.
  • It serves as a tool for filtering coherent structures in cellular automata.
  • Quantitative evidence supports particles (gliders, domain walls) as dominant information transfer agents.

Conclusions:

  • Local transfer entropy offers a powerful analytical tool for complex systems.
  • This measure validates the significant role of emergent structures in information propagation.
  • The findings have implications for understanding physical processes with analogous emergent phenomena.