Explicit Characterization of Performance of a Class of Networked Linear Control Systems

We quantify performance of a class of interconnected linear dynamical networks with arbitrary nodal dynamics. It is shown that the steady-state variance of the output, which is equivalent to the squared H 2 norm of the network, as a performance measure, can be expressed explicitly as a summation of...

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Bibliographic Details
Published in:IEEE transactions on control of network systems 2020-12, Vol.7 (4), p.1688-1699
Main Authors: Mousavi, Hossein K., Motee, Nader
Format: Article
Language:English
Subjects:
Control systems
Eigenvalues
Eigenvalues and eigenfunctions
Fundamental limits
Laplace equations
Linear control
Networked control systems
Networks
Noise measurement
Output feedback
performance measures
Rational functions
Robustness
Scaling laws
Vehicle dynamics
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Summary:We quantify performance of a class of interconnected linear dynamical networks with arbitrary nodal dynamics. It is shown that the steady-state variance of the output, which is equivalent to the squared H 2 norm of the network, as a performance measure, can be expressed explicitly as a summation of a rational function over the Laplacian eigenvalues of the underlying graph of the network. Our results generalize the existing works on H 2 -norm characterization for the first- and second-order consensus networks to general consensus-type linear dynamical networks with arbitrary nodal dynamics. We characterize several fundamental limits and scaling laws for the performance of this class of networks. To show the practical usefulness of our results, we discuss how to design decentralized observer-based output feedback mechanisms and how to analyze the performance of composite networks. Numerous examples support our theoretical contributions.
ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2020.2995825