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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control: 36 (Developments in Mathematics) - Tapa dura
<DIV>THIS MONOGRAPH CONTAINS AN IN-DEPTH ANALYSIS OF THE DYNAMICS GIVEN BY A LINEAR HAMILTONIAN SYSTEM OF GENERAL DIMENSION WITH NONAUTONOMOUS BOUNDED AND UNIFORMLY CONTINUOUS COEFFICIENTS, WITHOUT OTHER INITIAL ASSUMPTIONS ON TIME-RECURRENCE. PARTICULAR ATTENTION IS GIVEN TO THE OSCILLATION PROPERTIES OF THE SOLUTIONS AS WELL AS TO A SPECTRAL THEORY APPROPRIATE FOR SUCH SYSTEMS. THE BOOK CONTAINS EXTENSIONS OF RESULTS WHICH ARE WELL KNOWN WHEN THE COEFFICIENTS ARE AUTONOMOUS OR PERIODIC, AS WELL AS IN THE NONAUTONOMOUS TWO-DIMENSIONAL CASE. HOWEVER, A SUBSTANTIAL PART OF THE THEORY PRESENTED HERE IS NEW EVEN IN THOSE MUCH SIMPLER SITUATIONS.</DIV><DIV><BR></DIV><DIV>THE AUTHORS MAKE SYSTEMATIC USE OF BASIC FACTS CONCERNING LAGRANGE PLANES AND SYMPLECTIC MATRICES, AND APPLY SOME FUNDAMENTAL METHODS OF TOPOLOGICAL DYNAMICS AND ERGODIC THEORY. AMONG THE TOOLS USED IN THE ANALYSIS, WHICH INCLUDE LYAPUNOV EXPONENTS, WEYL MATRICES, EXPONENTIAL DICHOTOMY, AND WEAK DISCONJUGACY, A FUNDAMENTAL ROLE IS PLAYED BY THE ROTATION NUMBER FOR LINEAR HAMILTONIAN SYSTEMS OF GENERAL DIMENSION. THE PROPERTIES OF ALL THESE OBJECTS FORM THE BASIS FOR THE STUDY OF SEVERAL THEMES CONCERNING LINEAR-QUADRATIC CONTROL PROBLEMS, INCLUDING THE LINEAR REGULATOR PROPERTY, THE KALMAN-BUCY FILTER, THE INFINITE-HORIZON OPTIMIZATION PROBLEM, THE NONAUTONOMOUS VERSION OF THE YAKUBOVICH FREQUENCY THEOREM, AND DISSIPATIVITY IN THE WILLEMS SENSE.</DIV><DIV><BR></DIV><DIV>THE BOOK WILL BE USEFUL FOR GRADUATE STUDENTS AND RESEARCHERS INTERESTED IN NONAUTONOMOUS DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS AND ERGODIC THEORY; SPECTRAL THEORY OF DIFFERENTIAL OPERATORS; AND CONTROL THEORY.</DIV>
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This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations.
The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense.
The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.
The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense.
The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.
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- Año de publicación2016
- ISBN 10 3319290231
- ISBN 13 9783319290232
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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control (Developments in Mathematics) by Johnson, Russell, Obaya, Rafael, Novo, Sylvia, Núñez, Carmen, Fabbri, Roberta [Hardcover ]
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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control (Developments in Mathematics, 36)
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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
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Descripción Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations.The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense.The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory. 520 pp. Englisch. Nº de ref. del artículo: 9783319290232
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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
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Descripción Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Provides a detailed study of the concept of rotation and of the solutionsof linear nonautonomous Hamiltonian systems of general dimensionExplores the applications of linear Hamiltonian systems toquestions arising in classical oscillation theory of. Nº de ref. del artículo: 112308218
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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
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Descripción Buch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations.The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamentalrole is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense.The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory. Nº de ref. del artículo: 9783319290232
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