Methods of Algebraic Geometry in Control Theory: Part II: Multivariable Linear Systems and Projective Algebraic GeometrySpringer Science & Business Media, 1990 - 390 pàgines "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 time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro 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). |
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Methods of Algebraic Geometry in Control Theory: Part II: Multivariable ... Peter Falb Previsualització limitada - 2013 |
Methods of Algebraic Geometry in Control Theory: Part II: Multivariable ... Peter Falb Previsualització no disponible - 2000 |
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affine variety algebraic geometry algebraic set An²+n(m+p b₁ closed Consider coordinates coprime Corollary define Definition dimension divisor element equivalently Example finite follows G acts G-morphism geometric quotient given Gr(m Gr(p Grassmann equations H₁ H₂ Hank(n Hankel matrix Hankel(n hence homogeneous homogeneous ideal homomorphism hyperplane hypersurface implies induction injective integral domain intersection irreducible isomorphism k[Yo L₁ Lemma linear subspace linear system m₁ minimal realization modulo monic morphism Noetherian nonsingular open set ow,v polynomial prime ideal principal G-bundle projective variety Proof Proposition quasi-affine variety quasi-projective quasi-projective variety R-module rank Rat(n regular regular local ring relatively prime ring Sm,p space Spec(R subset subvariety Suppose surjective Theorem transfer matrix U₁ unimodular V₁ V₂ vector w₁ words X₁ Y₁
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Pàgina 379 - Grassmannian, central projection, and output feedback pole assignment of linear systems. IEEE Trans.
Pàgina 375 - Birkhoff, G. and Maclane, S., A Survey of Modern Algebra, Revised Edition, Macmillan, New York, 1953.
Pàgina 375 - Moduli and Canonical Forms for Linear Dynamical Systems III: The Algebraic-Geometric Case," in Geometric Control Theory (C.
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Systems and Control in the Twenty-First Century Christopher I. Byrnes,Biswa N. Datta,Clyde F. Martin Previsualització limitada - 1997 |