Methods of Algebraic Geometry in Control Theory: Part I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Algebraic Geometry in Control Theory: Part I write by Peter Falb. This book was released on 2018-08-25. Methods of Algebraic Geometry in Control Theory: Part I available in PDF, EPUB and Kindle. "An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik
Methods of Algebraic Geometry in Control Theory: Part II
Methods of Algebraic Geometry in Control Theory: Part II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Algebraic Geometry in Control Theory: Part II write by Peter Falb. This book was released on 2018-09-14. Methods of Algebraic Geometry in Control Theory: Part II available in PDF, EPUB and Kindle. "An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing mathematical rigor, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than on abstraction. While familiarity with Part I is helpful, it is not essential, since a considerable amount of relevant material is included here. Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains a clear presentation, with an applied flavor , of the core ideas in the algebra-geometric treatment of scalar linear system theory. Part II extends the theory to multivariable systems. After delineating limitations of the scalar theory through carefully chosen examples, the author introduces seven representations of a multivariable linear system and establishes the major results of the underlying theory. Of key importance is a clear, detailed analysis of the structure of the space of linear systems including the full set of equations defining the space. Key topics also covered are the Geometric Quotient Theorem and a highly geometric analysis of both state and output feedback. Prerequisites are the basics of linear algebra, some simple topological notions, the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises, which are an integral part of the exposition throughout, combined with an index and extensive bibliography of related literature make this a valuable classroom tool or good self-study resource. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input-, two-output systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." —Publicationes Mathematicae, Debrecen "This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I.... In the first volume the simpler single-input–single-output time-invariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory.... Each chapter contains illustrative examples throughout and terminates with some exercises for further study." —Mathematical Reviews
Methods of Algebraic Geometry in Control Theory
Methods of Algebraic Geometry in Control Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Algebraic Geometry in Control Theory write by Peter L. Falb. This book was released on 1990. Methods of Algebraic Geometry in Control Theory available in PDF, EPUB and Kindle.
Methods of Algebraic Geometry in Control Theory
Methods of Algebraic Geometry in Control Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Algebraic Geometry in Control Theory write by Peter Falb. This book was released on 2014-09-01. Methods of Algebraic Geometry in Control Theory available in PDF, EPUB and Kindle.
Methods of Algebraic Geometry in Control Theory: Part I
Methods of Algebraic Geometry in Control Theory: Part I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods of Algebraic Geometry in Control Theory: Part I write by Peter Falb. This book was released on 2012-06-12. Methods of Algebraic Geometry in Control Theory: Part I available in PDF, EPUB and Kindle. Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of these notes is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory. I began the development of these notes over fifteen years ago with a series of lectures given to the Control Group at the Lund Institute of Technology in Sweden. Over the following years, I presented the material in courses at Brown several times and must express my appreciation for the feedback (sic!) received from the students. I have attempted throughout to strive for clarity, often making use of constructive methods and giving several proofs of a particular result. Since algebraic geometry draws on so many branches of mathematics and can be dauntingly abstract, it is not easy to convey its beauty and utility to those interested in applications. I hope at least to have stirred the reader to seek a deeper understanding of this beauty and utility in control theory. The first volume dea1s with the simplest control systems (i. e. single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i. e. affine algebraic geometry).
