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Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Lyapunov stability --- Energy dissipation --- Dynamics --- Large scale systems --- Information Technology --- General and Others --- Lyapunov stability. --- Energy dissipation. --- Dynamics. --- Large scale systems. --- Systems, Large scale --- Dynamical systems --- Kinetics --- Liapunov stability --- Ljapunov stability --- Degradation, Energy --- Dissipation (Physics) --- Energy degradation --- Energy losses --- Losses, Energy --- Engineering systems --- System analysis --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Control theory --- Stability --- Clausius-type inequality. --- KalmanЙakubovichАopov conditions. --- KalmanЙakubovichАopov equations. --- KrasovskiiЌaSalle theorem. --- asymptotic stabilizability. --- combustion processes. --- comparison system. --- compartmental dynamical system theory. --- compartmental dynamical system. --- control Lyapunov function. --- control design. --- control signal. --- control vector Lyapunov function. --- convergence. --- coordination control. --- decentralized affine. --- decentralized control. --- decentralized controller. --- decentralized finite-time stabilizer. --- discrete-time dynamical system. --- dissipativity theory. --- dynamical system. --- ectropy. --- energy conservation. --- energy dissipation. --- energy equipartition. --- energy flow. --- entropy. --- feedback control law. --- feedback interconnection stability. --- feedback stabilizer. --- finite-time stability. --- finite-time stabilization. --- gain margin. --- hybrid closed-loop system. --- hybrid decentralized controller. --- hybrid dynamic controller. --- hybrid finite-time stabilizing controller. --- hybrid vector comparison system. --- hybrid vector dissipation inequality. --- impulsive differential equations. --- impulsive dynamical system. --- interconnected dynamical system. --- large-scale dynamical system. --- law of thermodynamics. --- linear energy exchange. --- maximum entropy control. --- multiagent interconnected system. --- multiagent systems. --- multivehicle coordinated motion control. --- nonconservation of ectropy. --- nonconservation of entropy. --- nonlinear dynamical system. --- optimality. --- plant energy. --- scalar Lyapunov function. --- sector margin. --- semistable dissipation matrix. --- stability analysis. --- stability theory. --- stability. --- state space. --- subsystem decomposition. --- subsystem energy. --- thermoacoustic instabilities. --- thermodynamic modeling. --- time-invariant set. --- time-varying set. --- vector Lyapunov function. --- vector available storage. --- vector comparison system. --- vector dissipation inequality. --- vector dissipative system. --- vector dissipativity theory. --- vector dissipativity. --- vector field. --- vector hybrid supply rate. --- vector lossless system. --- vector required supply. --- vector storage function. --- vector supply rate.

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This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.

Thermodynamics --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Mathematics. --- Addition. --- Adiabatic process. --- Applied mathematics. --- Arthur Eddington. --- Asymmetry. --- Available energy (particle collision). --- Axiom. --- Balance equation. --- Banach space. --- Boltzmann's entropy formula. --- Brillouin scattering. --- Carnot cycle. --- Classical mechanics. --- Clausius (crater). --- Compact space. --- Conservation law. --- Conservation of energy. --- Constant of integration. --- Continuous function (set theory). --- Continuous function. --- Control theory. --- Deformation (mechanics). --- Derivative. --- Diathermal wall. --- Diffeomorphism. --- Differentiable function. --- Diffusion process. --- Dimension (vector space). --- Dimension. --- Dissipation. --- Dot product. --- Dynamical system. --- Emergence. --- Energy density. --- Energy level. --- Energy storage. --- Energy. --- Entropy. --- Equation. --- Equations of motion. --- Equilibrium point. --- Equilibrium thermodynamics. --- Equipartition theorem. --- Existential quantification. --- First law of thermodynamics. --- Hamiltonian mechanics. --- Heat capacity. --- Heat death of the universe. --- Heat flux. --- Heat transfer. --- Homeomorphism. --- Hydrogen atom. --- Ideal gas. --- Inequality (mathematics). --- Infimum and supremum. --- Infinitesimal. --- Initial condition. --- Instant. --- Internal energy. --- Irreversible process. --- Isolated system. --- Kinetic theory of gases. --- Laws of thermodynamics. --- Linear dynamical system. --- Lipschitz continuity. --- Local boundedness. --- Lyapunov function. --- Lyapunov stability. --- Mathematical optimization. --- Molecule. --- Non-equilibrium thermodynamics. --- Operator norm. --- Probability. --- Quantity. --- Reversible process (thermodynamics). --- Second law of thermodynamics. --- Semi-infinite. --- Smoothness. --- State variable. --- State-space representation. --- Statistical mechanics. --- Steady state. --- Summation. --- Supply (economics). --- Systems theory. --- Temperature. --- Theorem. --- Theoretical physics. --- Theory. --- Thermal conduction. --- Thermal equilibrium. --- Thermodynamic equilibrium. --- Thermodynamic process. --- Thermodynamic state. --- Thermodynamic system. --- Thermodynamic temperature. --- Thermodynamics. --- Time evolution. --- Zeroth law of thermodynamics.

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Pure sciences. Natural sciences (general)