Well-Posed Linear Systems
Author: Olof J. Staffans
Publisher: Cambridge University Press
Published: 2005-02-24
Total Pages: 795
ISBN-13: 0521825849
DOWNLOAD EBOOKPublisher Description
Read and Download eBook Full
Author: Olof J. Staffans
Publisher: Cambridge University Press
Published: 2005-02-24
Total Pages: 795
ISBN-13: 0521825849
DOWNLOAD EBOOKPublisher Description
Author: Olof Staffans
Publisher: Cambridge University Press
Published: 2005-02-24
Total Pages: 804
ISBN-13: 9781139442237
DOWNLOAD EBOOKMany infinite-dimensional linear systems can be modelled in a Hilbert space setting. Others, such as those dealing with heat transfer or population dynamics, need to be set more generally in Banach spaces. This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting. It is also the first to describe the class of non-well-posed systems induced by system nodes. The author shows how standard finite-dimensional results from systems theory can be extended to these more general classes of systems, and complements them with new results which have no finite-dimensional counterpart. Much of the material presented is original, and many results have never appeared in book form before. A comprehensive bibliography rounds off this work which will be indispensable to all working in systems theory, operator theory, delay equations and partial differential equations.
Author: Petrov Yuri P.
Publisher: Walter de Gruyter
Published: 2011-12-22
Total Pages: 245
ISBN-13: 3110195305
DOWNLOAD EBOOKThis book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.
Author: Philip E. Sarachik
Publisher: Cambridge University Press
Published: 1997-01-28
Total Pages: 300
ISBN-13: 9780521576062
DOWNLOAD EBOOKA textbook on state-space methods in the analysis of linear multi-input, multi-output dynamic systems.
Author: Tatsuo Nishitani
Publisher: Springer
Published: 2013-11-19
Total Pages: 245
ISBN-13: 3319022733
DOWNLOAD EBOOKThis monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contain strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearby.
Author: Ferenc Szidarovszky
Publisher: Routledge
Published: 2018-05-03
Total Pages: 530
ISBN-13: 1351435191
DOWNLOAD EBOOKThis second edition comprehensively presents important tools of linear systems theory, including differential and difference equations, Laplace and Z transforms, and more. Linear Systems Theory discusses: Nonlinear and linear systems in the state space form and through the transfer function method Stability, including marginal stability, asymptotical stability, global asymptotical stability, uniform stability, uniform exponential stability, and BIBO stability Controllability Observability Canonical forms System realizations and minimal realizations, including state space approach and transfer function realizations System design Kalman filters Nonnegative systems Adaptive control Neural networks The book focuses mainly on applications in electrical engineering, but it provides examples for most branches of engineering, economics, and social sciences. What's New in the Second Edition? Case studies drawn mainly from electrical and mechanical engineering applications, replacing many of the longer case studies Expanded explanations of both linear and nonlinear systems as well as new problem sets at the end of each chapter Illustrative examples in all the chapters An introduction and analysis of new stability concepts An expanded chapter on neural networks, analyzing advances that have occurred in that field since the first edition Although more mainstream than its predecessor, this revision maintains the rigorous mathematical approach of the first edition, providing fast, efficient development of the material. Linear Systems Theory enables its reader to develop his or her capabilities for modeling dynamic phenomena, examining their properties, and applying them to real-life situations.
Author: Alexander Givental
Publisher: American Mathematical Soc.
Published: 2001
Total Pages: 150
ISBN-13: 9780821828502
DOWNLOAD EBOOKThe material presented in this book corresponds to a semester-long course, ``Linear Algebra and Differential Equations'', taught to sophomore students at UC Berkeley. In contrast with typical undergraduate texts, the book offers a unifying point of view on the subject, namely that linear algebra solves several clearly-posed classification problems about such geometric objects as quadratic forms and linear transformations. This attractive viewpoint on the classical theory agrees well with modern tendencies in advanced mathematics and is shared by many research mathematicians. However, the idea of classification seldom finds its way to basic programs in mathematics, and is usually unfamiliar to undergraduates. To meet the challenge, the book first guides the reader through the entire agenda of linear algebra in the elementary environment of two-dimensional geometry, and prior to spelling out the general idea and employing it in higher dimensions, shows how it works in applications such as linear ODE systems or stability of equilibria. Appropriate as a text for regular junior and honors sophomore level college classes, the book is accessible to high school students familiar with basic calculus, and can also be useful to engineering graduate students.
Author: Ben M. Chen
Publisher: Springer Science & Business Media
Published: 2004-08-27
Total Pages: 440
ISBN-13: 9780817637798
DOWNLOAD EBOOKIncludes MATLAB-based computational and design algorithms utilizing the "Linear Systems Toolkit." All results and case studies presented in both the continuous- and discrete-time settings.
Author: Panos J. Antsaklis
Publisher: Springer Science & Business Media
Published: 2007-12-03
Total Pages: 524
ISBN-13: 0817646612
DOWNLOAD EBOOKBased on a streamlined presentation of the authors’ successful work Linear Systems, this textbook provides an introduction to systems theory with an emphasis on control. Initial chapters present necessary mathematical background material for a fundamental understanding of the dynamical behavior of systems. Each chapter includes helpful chapter descriptions and guidelines for the reader, as well as summaries, notes, references, and exercises at the end. The emphasis throughout is on time-invariant systems, both continuous- and discrete-time.
Author: Jarmo Malinen
Publisher:
Published: 1997
Total Pages: 42
ISBN-13: 9789512236534
DOWNLOAD EBOOK