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BIBO stability of continuous and discrete -time systems

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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Related Experiment Video

Updated: May 27, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

A novel chaotic system with one absolute term: stability, ultimate boundedness, and image encryption.

Ali A Shukur¹, Ammar Ali Neamah¹, Viet-Thanh Pham²

¹Faculty of Computer Sciences and Mathematics, University of Kufa, Iraq.

|February 17, 2025

Summary

A novel chaotic system with nested attractors is introduced for secure applications. When combined with a Toeplitz matrix, it creates a robust encryption algorithm highly resistant to attacks.

Keywords:

37M05 37N35 65P20 Chaotic system Image encryption Security Toeplitz matrix Ultimate bounds

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Area of Science:

* Applied Mathematics
* Cryptography
* Chaos Theory

Background:

* Chaotic systems offer potential for secure data encryption.
* Existing encryption methods face evolving security challenges.
* The need for robust, computationally efficient algorithms is critical.

Purpose of the Study:

* To propose a new chaotic system with unique attractor properties.
* To develop a secure image encryption algorithm using this system and a Toeplitz matrix.
* To evaluate the algorithm's security and performance against existing methods.

Main Methods:

* Analysis of system dynamics using bifurcation diagrams and Lyapunov exponents.
* Integration of the chaotic system with a Toeplitz matrix for encryption.
* Comprehensive security analysis, including resistance to differential and statistical attacks.
* Performance evaluation through comparative assessment.

Main Results:

* The proposed system exhibits a countable finite number of coexisting nested attractors.
* The combined encryption algorithm demonstrates enhanced pixel distribution randomness.
* The algorithm proved impervious to various cryptanalytic attacks.
* Superior performance compared to previously reported encryption techniques.

Conclusions:

* The developed chaotic system and encryption algorithm provide a highly secure solution.
* The approach offers improved randomness and robustness for image encryption.
* This method presents a significant advancement in secure communication systems.