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BIBO stability of continuous and discrete -time systems01:24

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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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    Area of Science:

    • Complex dynamical systems
    • Neural network theory
    • Control theory

    Background:

    • Synchronization is crucial for complex-valued delayed neural networks.
    • Existing methods often require separating networks into real and imaginary parts, which is complex.
    • Discontinuous activations and time-varying delays pose significant challenges.

    Purpose of the Study:

    • To develop novel methods for finite and fixed-time synchronization of complex-valued delayed neural networks.
    • To avoid the separation of complex networks into real subsystems.
    • To propose discontinuous control strategies and analyze synchronization criteria.

    Main Methods:

    • A novel complex-valued sign function was proposed and its properties established.
    • Two discontinuous control strategies were developed using quadratic and a new absolute-value-based norm.
    • Nonsmooth analysis and novel inequality techniques in the complex field were applied.

    Main Results:

    • Synchronization criteria and settling time estimates were derived for complex-valued delayed neural networks.
    • A unified control strategy was designed under the new norm framework.
    • A single controller parameter was found to determine finite or fixed-time synchronization.

    Conclusions:

    • The proposed methods effectively achieve finite and fixed-time synchronization without network separation.
    • The novel norm and control strategy offer a unified approach to synchronization.
    • The findings contribute to the theoretical understanding and practical control of complex dynamical systems.