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Control theory. --- Differentiable dynamical systems. --- Digital filters (Mathematics). --- Neural networks (Computer science). --- Nonlinear theories.

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In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.

Differentiable dynamical systems. --- Stability. --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Global analysis (Mathematics). --- System theory. --- Differential Equations. --- Differential equations, partial. --- Functional equations. --- Analysis. --- Systems Theory, Control. --- Control, Robotics, Mechatronics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Difference and Functional Equations. --- Equations, Functional --- Functional analysis --- Partial differential equations --- 517.91 Differential equations --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory. --- Mathematical analysis. --- Analysis (Mathematics). --- Control engineering. --- Robotics. --- Mechatronics. --- Differential equations. --- Partial differential equations. --- Difference equations. --- 517.1 Mathematical analysis --- Mathematical analysis --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Automatic control. --- Differential equations, Partial.

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The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems.  For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonicLyapunov functions.Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks.   The authors cover the following four general topics:   -          Representation and modeling of dynamical systems of the types described above -          Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces involving monotonic and non-monotonic Lyapunov functions -          Specialization of this stability theory to finite-dimensional dynamical systems -          Specialization of this stability theory to infinite-dimensional dynamical systems   Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this bookcan be used as a textbook for graduate courses in stability theory of dynamical systems.  It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences.   Review of the First Edition:   “The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems.  [This] is a very interesting book which complements the existing literature. [It] is clearly written, and difficult concepts are illustrated by means of good examples.”   - Alessandro Astolfi, IEEE Control Systems Magazine, February 2009.

Mathematics. --- Systems Theory, Control. --- Control, Robotics, Mechatronics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Difference and Functional Equations. --- Functional equations. --- Differential Equations. --- Differential equations, partial. --- Systems theory. --- Mathématiques --- Equations fonctionnelles --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Difference equations. --- Differential equations. --- Partial differential equations. --- System theory. --- Control engineering. --- Robotics. --- Mechatronics. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Equations, Functional --- Functional analysis --- Differentiable dynamical systems. --- Stability. --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Systems, Theory of --- Systems science --- Science --- Philosophy

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"There are three words that characterize this work: thoroughness, completeness and clarity. The authors are congratulated for taking the time to write an excellent linear systems textbook! …The authors have used their mastery of the subject to produce a textbook that very effectively presents the theory of linear systems as it has evolved over the last thirty years. The result is a comprehensive, complete and clear exposition that serves as an excellent foundation for more advanced topics in system theory and control." —IEEE Transactions on Automatic Control "In assessing the present book as a potential textbook for our first graduate linear systems course, I find...[that] Antsaklis and Michel have contributed an expertly written and high quality textbook to the field and are to be congratulated…. Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference." —Automatica Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook. The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systems and control. Linear Systems is written as a textbook for a challenging one-semester graduate course; a solutions manual is available to instructors upon adoption of the text. The book’s flexible coverage and self-contained presentation also make it an excellent reference guide or self-study manual. ******* For a treatment of linear systems that focuses primarily on the time-invariant case using streamlined presentation of the material with less formal and more intuitive proofs, see the authors’ companion book entitled A Linear Systems Primer.

Linear control systems --- Control theory --- Signal processing --- Mathematical control systems --- Ordinary differential equations --- Linear control systems. --- Control theory. --- Signal processing. --- Processing, Signal --- Engineering. --- System theory. --- Computer mathematics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Control engineering. --- Robotics. --- Mechatronics. --- Electronic circuits. --- Control. --- Circuits and Systems. --- Vibration, Dynamical Systems, Control. --- Control, Robotics, Mechatronics. --- Systems Theory, Control. --- Computational Science and Engineering. --- Information measurement --- Signal theory (Telecommunication) --- Dynamics --- Machine theory --- Automatic control --- Systems engineering. --- Systems theory. --- Computer science. --- Control and Systems Theory. --- Engineering systems --- System engineering --- Engineering --- Industrial engineering --- System analysis --- Informatics --- Science --- Cycles --- Mechanics --- Sound --- Systems, Theory of --- Systems science --- Design and construction --- Philosophy --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Electron-tube circuits --- Electric circuits --- Electron tubes --- Electronics --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Computer mathematics --- Electronic data processing --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automatic control. --- Computer science --- Mathematics.

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In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above* Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces* Specialization of this stability theory to finite-dimensional dynamical systems* Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics. [Publisher]

Differentiable dynamical systems --- Stability --- Differentiable dynamical systems. --- Stability. --- Dynamique différentiable --- Systèmes dynamiques --- Stabilité --- 517.9 --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Dynamique différentiable. --- Systèmes dynamiques. --- Stabilité.