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Root Loci for Positive-Feedback Systems01:23

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The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Reaching Non-Negative Edge Consensus of Networked Dynamical Systems.

Xiao Ling Wang, Housheng Su, Michael Z Q Chen

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    Summary
    This summary is machine-generated.

    This study develops a distributed algorithm for non-negative edge consensus in networked systems. The research provides conditions for consensus and demonstrates a low-gain feedback technique effective even with input saturation.

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    Area of Science:

    • Control Systems Engineering
    • Networked Systems Theory
    • Distributed Algorithms

    Background:

    • Networked linear time-invariant systems require consensus algorithms for coordinated behavior.
    • Achieving non-negative edge consensus is crucial for applications like resource allocation and synchronization.

    Purpose of the Study:

    • To address the problem of non-negative edge consensus in undirected networked linear time-invariant systems.
    • To develop a distributed algorithm and derive sufficient conditions for achieving this consensus.

    Main Methods:

    • Associating each network edge with a state variable and constructing a distributed algorithm.
    • Deriving sufficient conditions based on the number of edges.
    • Employing linear programming and low-gain feedback for controller design.

    Main Results:

    • Sufficient conditions for non-negative edge consensus were established, depending solely on the number of edges.
    • A simplified design of the feedback gain matrix was achieved using linear programming and low-gain feedback.
    • The low-gain feedback technique proved effective for systems with input saturation.

    Conclusions:

    • The proposed distributed algorithm and derived conditions effectively achieve non-negative edge consensus.
    • The low-gain feedback technique offers a robust and simplified approach, particularly for systems with input saturation.
    • Numerical simulations validated the theoretical findings and the practical applicability of the methods.