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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.
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A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
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Transfer Function to State Space01:23

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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.
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Related Experiment Video

Updated: Jan 30, 2026

Imaging Approaches to Assessments of Toxicological Oxidative Stress Using Genetically-encoded Fluorogenic Sensors
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A Common Assessment Space for Different Sensor Structures.

Wei Wen1, Ondřej Kajínek2, Siamak Khatibi3

  • 1Department of Technology and Aesthetics, Blekinge Institute of Technology, 37179 Karlskrona, Sweden. wei.wen@bth.se.

Sensors (Basel, Switzerland)
|February 1, 2019
PubMed
Summary
This summary is machine-generated.

Researchers developed a common space to compare rectangular and hexagonal sensor arrangements. This method allows direct assessment of differences, revealing hexagonal images offer richer intensity variation and dynamic range.

Keywords:
common spacecontinuous extensionhexagonal imagepixel arrangementpixel formresamplingsoftware-based

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Area of Science:

  • Computer Vision
  • Image Processing
  • Sensory Systems

Background:

  • The human visual system exhibits varied spatial arrangements, from hexagonal in the fovea to sparse in the periphery.
  • Current image sensors are limited to rectangular and hexagonal arrangements, hindering direct comparison.
  • A method is needed to assess differences between sensor spatial arrangements without data conversion.

Purpose of the Study:

  • To propose a novel method for creating a common space to analyze and compare diverse spatial arrangements.
  • To enable direct assessment of differences between rectangular and hexagonal sensor arrangements.

Main Methods:

  • Implemented a continuous extension of the discrete Weyl Group orbit function transform.
  • Generated hexagonal images from rectangular images using half-pixel shifting and virtual hexagonal methods.
  • Assessed differences between original rectangular and generated hexagonal images within the common space.

Main Results:

  • The common space facilitates a user-friendly tool for analyzing spatial arrangements.
  • Hexagonal images demonstrated richer intensity variation compared to rectangular images.
  • Hexagonal images exhibited nonlinear behavior and a larger dynamic range than rectangular images.

Conclusions:

  • The proposed common space effectively allows for the direct assessment of differences between various spatial arrangements.
  • This approach provides valuable insights into the performance characteristics of different sensor layouts.
  • Hexagonal arrangements show potential advantages in capturing image intensity and dynamic range.