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    This study introduces a delay-dependent algebraic Riccati equation (DARE) method for stabilizing networked control systems with signal delays and attenuation. It establishes new conditions for stability and derives the maximum allowable delay for systems.

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    Area of Science:

    • Control Systems Engineering
    • Systems Theory
    • Networked Systems

    Background:

    • Networked control systems (NCS) often involve communication delays and signal attenuation.
    • Previous studies frequently assumed ideal transmission with zero delay and infinite precision.
    • Real-world NCS require addressing practical constraints like simultaneous delay and attenuation.

    Purpose of the Study:

    • To develop a delay-dependent algebraic Riccati equation (DARE) approach for mean-square stabilization of continuous-time NCS.
    • To address the challenges of signal attenuation and transmission delay in control signal communication.
    • To establish novel theoretical conditions and methods for analyzing NCS stability under these constraints.

    Main Methods:

    • Utilizing a delay-dependent algebraic Riccati equation (DARE) framework.
    • Applying operator spectrum theory to analyze the stabilizing solutions of DAREs.
    • Defining a delay-dependent Lyapunov operator for existence theorems.
    • Deriving explicit maximal allowable delay bounds for scalar systems.

    Main Results:

    • A necessary and sufficient condition for mean-square stabilization is established, based on a unique positive definite solution to a DARE.
    • The Lyapunov/spectrum stabilizing criterion is derived from this condition.
    • An existence theorem for a unique stabilizing solution to a generalized DARE is proposed using a delay-dependent Lyapunov operator.
    • The explicit maximal allowable delay bound for a scalar system is derived.

    Conclusions:

    • The proposed DARE approach provides a robust framework for analyzing and stabilizing NCS with communication constraints.
    • The derived conditions and methods offer theoretical guarantees for system stability under delay and attenuation.
    • The results are validated through illustrative examples, confirming the practical applicability of the theoretical findings.