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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Practical Fixed-Time Control of Switched Neutral Filippov Systems on Networks.

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    This summary is machine-generated.

    This study introduces practical fixed-time control for switched neutral Filippov systems, enhancing stability analysis with novel Lyapunov inequalities and addressing real-world limitations for accurate state convergence.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems Analysis
    • Networked Systems

    Background:

    • Switched neutral Filippov systems (SNFSs) present challenges due to discontinuous perturbations and neutral logics.
    • Existing finite-time control methods often lack practical accuracy in state convergence for real-world applications.

    Purpose of the Study:

    • To develop practical fixed-time (FxT) control strategies for SNFSs on networks.
    • To establish novel stability analysis techniques for systems with discontinuous perturbations and delays.
    • To address the limitations of existing finite-time control in achieving accurate state convergence.

    Main Methods:

    • Development of new Lyapunov inequalities with indefinite functions for settling-time (ST) estimation.
    • Establishment of practical FxT stability lemmas with bounded indefinite functions.
    • Design of adaptive control strategies using Lyapunov-Krasovskii functionals (LKFs) to handle system delays.

    Main Results:

    • Novel Lyapunov inequalities provide detailed ST estimations, encompassing existing results.
    • Practical FxT stability lemmas with bounded indefinite functions are introduced for the first time.
    • Adaptive control successfully achieves FxT and practical FxT synchronization for SNFSs with delays.
    • A theoretical deficiency in FxT stability analysis for delayed systems using Lyapunov functions is resolved.

    Conclusions:

    • The proposed methods offer a more practical approach to FxT control for SNFSs, especially in networked environments.
    • The study overcomes key theoretical and practical challenges in analyzing and controlling delayed SNFSs.
    • Numerical simulations on an LC transmission line validate the effectiveness of the developed control strategies.