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# ðŸ“™ Methods of Algebraic Geometry in Control Theory: Part II: Multivariable Linear Systems and Projective Algebraic Geometry by Peter Falb (auth.) â€” free epub

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"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 this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt 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). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear timeÂ invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and proÂ jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).

- Series:
**Systems & Control: Foundations & Applications** - Author:
**Peter Falb (auth.)** - Year:
**1999** - Publisher:
**BirkhÃ¤user Basel** - Language:
**English** - ISBN:
**978-1-4612-7194-9,978-1-4612-1564-6**

- File size:
**8 682 323** - Format:
**pdf**

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Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many o...

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This book is a collection of invited chapters covering several areas of modern sliding mode control theory. The authors identify key contributions defining the theoretical and applicative state of the art of the sliding mode control theory and the most pr...

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This book is a collection of invited chapters covering several areas of modern sliding mode control theory. The authors identify key contributions defining the theoretical and applicative state of the art of the sliding mode control theory and the most pr...

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The He...

During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a natural outflow of this research, this book presents information on this interdisciplinary area. The ...