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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 for Discrete-Time Large-Scale Dynamical Systems

Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical Systems

Chapter:
(p.181) Chapter Nine Thermodynamic Modeling for Discrete-Time Large-Scale Dynamical 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/9780691153469.003.0009

This chapter describes the thermodynamic modeling of discrete-time large-scale dynamical systems. In particular, it develops nonlinear discrete-time compartmental models that are consistent with thermodynamic principles. Since thermodynamic models are concerned with energy flow among subsystems, the chapter constructs a nonlinear compartmental dynamical system model characterized by conservation of energy and the first law of thermodynamics. It then provides a deterministic definition of entropy for a large-scale dynamical system that is consistent with the classical thermodynamic definition of entropy and shows that it satisfies a Clausius-type inequality leading to the law of entropy nonconservation. The chapter also considers nonconservation of entropy and the second law of thermodynamics, nonconservation of ectropy, semistability of discrete-time thermodynamic models, entropy increase and the second law of thermodynamics, and thermodynamic models with linear energy exchange.

Keywords:   thermodynamic modeling, large-scale dynamical system, energy flow, compartmental dynamical system, energy conservation, law of thermodynamics, nonconservation of entropy, nonconservation of ectropy, linear energy exchange

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