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Related Concept Videos

Transfer Function to State Space01:23

Transfer Function to State Space

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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.
In an RLC...
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State Space to Transfer Function01:21

State Space to Transfer Function

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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:
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State Space Representation01:27

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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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Seminormed double sequence spaces of four-dimensional matrix and Musielak-Orlicz function.

Renu Anand1, Charu Sharma1, Kuldip Raj1

  • 1School of Mathematics, Shri Mata Vaishno Devi University, Katra, India.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary

This study examines seminormed double sequence spaces using four-dimensional matrices and Musielak-Orlicz functions in n-normed spaces. Researchers investigated inclusion relations and algebraic/topological properties.

Keywords:
40A0540A9946A30

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Area of Science:

  • Functional Analysis
  • Sequence Space Theory
  • Topological Vector Spaces

Background:

  • Seminormed spaces are fundamental in functional analysis.
  • Sequence spaces are crucial for understanding convergence and structure.
  • Musielak-Orlicz functions provide a generalized framework for studying sequence spaces.

Purpose of the Study:

  • To introduce and analyze novel seminormed double sequence spaces.
  • To investigate the structure of these spaces using four-dimensional matrices.
  • To explore the behavior of Musielak-Orlicz functions within n-normed spaces.

Main Methods:

  • Utilizing the theory of n-normed spaces.
  • Applying concepts from four-dimensional matrix transformations.
  • Employing Musielak-Orlicz function theory for space construction.

Main Results:

  • Established key inclusion relations between the defined sequence spaces.
  • Characterized the algebraic properties (e.g., linearity, completeness) of these spaces.
  • Determined significant topological properties, such as convergence and boundedness.

Conclusions:

  • The newly defined seminormed double sequence spaces exhibit rich structural properties.
  • The interplay between matrices, Musielak-Orlicz functions, and n-normed spaces offers a generalized perspective.
  • Further research can extend these findings to other types of sequence spaces.