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    This study introduces annular finite-time H2/H∞ control for complex jump-diffusion systems. The new method ensures system stability and optimizes performance indices, outperforming existing finite-time control strategies.

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    Area of Science:

    • Control Theory
    • Stochastic Systems
    • Nonlinear Dynamics

    Background:

    • Mean-field jump-diffusion systems (MFJDSs) involve both continuous (Wiener) and discrete (Poisson) noise processes.
    • Ensuring finite-time stability and performance in such complex systems is a significant challenge.

    Purpose of the Study:

    • Introduce and analyze annular finite-time H2/H∞ control for MFJDSs.
    • Develop novel conditions for state feedback and observer-based annular finite-time H2/H∞ control.
    • Propose a new algorithm for parameter analysis and performance optimization.

    Main Methods:

    • Definition of annular finite-time bounded-ness (AFTB) in the mean-square sense.
    • Derivation of sufficient conditions for state feedback and observer-based control.
    • Development of an algorithm for determining stability parameters and performance trade-offs.

    Main Results:

    • The proposed annular finite-time H2/H∞ control ensures AFTB and minimizes H2/H∞ indices.
    • Less conservative conditions for state feedback and observer-based control are established.
    • The devised algorithm effectively determines stability ranges and performance relationships.

    Conclusions:

    • The novel annular finite-time H2/H∞ control offers superior performance for MFJDSs.
    • The proposed methodologies and algorithm provide practical tools for system design and analysis.
    • Demonstrated practical advantages through a comprehensive design example.