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Stability and Control of Large-Scale Dynamical SystemsA Vector Dissipative Systems Approach$
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Wassim M. Haddad and Sergey G. Nersesov

Print publication date: 2011

Print ISBN-13: 9780691153469

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153469.001.0001

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Thermodynamic Modeling of Large-Scale Interconnected Systems

Thermodynamic Modeling of Large-Scale Interconnected Systems

Chapter:
(p.75) Chapter Four Thermodynamic Modeling of Large-Scale Interconnected Systems
Source:
Stability and Control of Large-Scale Dynamical Systems
Author(s):

Wassim M. Haddad

Sergey G. Nersesov

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153469.003.0004

This chapter describes the thermodynamic modeling of large-scale interconnected dynamical systems. Using compartmental dynamical system theory, it develops energy flow models possessing energy conservation and energy equipartition principles for large-scale dynamical systems. It then gives a deterministic definition of entropy for a large-scale dynamical system that is consistent with the classical definition of entropy and shows that it satisfies a Clausius-type inequality leading to the law of nonconservation of entropy. It also introduces the notion of ectropy as a measure of the tendency of a dynamical system to do useful work and grow more organized. It demonstrates how conservation of energy in an isolated thermodynamic large-scale system leads to nonconservation of ectropy and entropy. Finally, the chapter uses the system ectropy as a Lyapunov function candidate to show that the large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.

Keywords:   thermodynamic modeling, interconnected dynamical system, compartmental dynamical system theory, energy flow, energy conservation, energy equipartition, entropy, Clausius-type inequality, nonconservation of entropy, ectropy

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