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BIBO stability of continuous and discrete -time systems01:24

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.
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The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
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Reliably Engineering and Controlling Stable Optogenetic Gene Circuits in Mammalian Cells
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Consistent stabilizability of switched Boolean networks.

Haitao Li1, Yuzhen Wang

  • 1School of Control Science and Engineering, Shandong University, Jinan 250061, PR China. haitaoli09@gmail.com

Neural Networks : the Official Journal of the International Neural Network Society
|June 22, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new algebraic method for analyzing switched Boolean networks (SBNs), offering effective strategies for designing switching signals to ensure consistent stabilizability, even with state constraints.

Keywords:
Consistent stabilizabilitySemi-tensor productState constraintSwitched Boolean network

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Area of Science:

  • Control theory
  • Boolean networks
  • Networked systems

Background:

  • Switched Boolean networks (SBNs) are crucial for modeling complex systems.
  • Ensuring consistent stabilizability in SBNs is a significant challenge.
  • Existing methods often lack comprehensive solutions for state-constrained SBNs.

Purpose of the Study:

  • To investigate the consistent stabilizability of switched Boolean networks (SBNs).
  • To develop novel algebraic conditions for designing switching signals.
  • To address SBNs with state constraints.

Main Methods:

  • Utilizing the semi-tensor product method for algebraic expression of SBNs.
  • Deriving necessary and sufficient conditions for switching signal design.
  • Applying the method to SBNs with state constraints.

Main Results:

  • An algebraic framework for SBNs using the semi-tensor product.
  • New conditions for designing free-form and state-feedback switching signals.
  • Effective conditions for consistent stabilizability of state-constrained SBNs.

Conclusions:

  • The semi-tensor product method provides an effective approach for SBN analysis.
  • The derived conditions facilitate the design of stabilizing switching signals.
  • The results are applicable to a broader range of SBNs, including those with state constraints.