LEADER 06128nam 22005655 450 001 9910300139203321 005 20200630131627.0 010 $a3-319-96574-3 024 7 $a10.1007/978-3-319-96574-1 035 $a(CKB)4100000006674918 035 $a(DE-He213)978-3-319-96574-1 035 $a(MiAaPQ)EBC6311503 035 $a(PPN)230537995 035 $a(EXLCZ)994100000006674918 100 $a20180914d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMethods of Algebraic Geometry in Control Theory: Part II $eMultivariable Linear Systems and Projective Algebraic Geometry /$fby Peter Falb 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (X, 390 p. 3 illus.) 225 1 $aModern Birkhäuser Classics,$x2197-1803 311 $a3-319-96573-5 327 $a1 Scalar Input or Scalar Output Systems -- 2 Two or Three Input, Two Output Systems: Some Examples -- 3 The Transfer and Hankel Matrices -- 4 Polynomial Matrices -- 5 Projective Space -- 6 Projective Algebraic Geometry I: Basic Concepts -- 7 Projective Algebraic Geometry II: Regular Functions, Local Rings, Morphisms -- 8 Exterior Algebra and Grassmannians -- 9 The Laurent Isomorphism Theorem: I -- 10 Projective Algebraic Geometry III: Products, Graphs, Projections -- 11 The Laurent Isomorphism Theorem: II -- 12 Projective Algebraic Geometry IV: Families, Projections, Degree -- 13 The State Space: Realizations, Controllability, Observability, Equivalence -- 14 Projective Algebraic Geometry V: Fibers of Morphisms -- 15 Projective Algebraic Geometry VI: Tangents, Differentials, Simple Subvarieties -- 16 The Geometric Quotient Theorem -- 17 Projective Algebraic Geometry VII: Divisors -- 18 Projective Algebraic Geometry VIII: Intersections -- 19 State Feedback -- 20 Output Feedback -- Appendices -- A Formal Power Series, Completions, Regular Local Rings, and Hubert Polynomials -- B Specialization, Generic Points and Spectra -- C Differentials -- D The Space -- E Review of Affine Algebraic Geometry -- References -- Glossary of Notations. 330 $a"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. 410 0$aModern Birkhäuser Classics,$x2197-1803 606 $aSystem theory 606 $aAlgebraic geometry 606 $aControl engineering 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 615 0$aSystem theory. 615 0$aAlgebraic geometry. 615 0$aControl engineering. 615 14$aSystems Theory, Control. 615 24$aAlgebraic Geometry. 615 24$aControl and Systems Theory. 676 $a629.8312 700 $aFalb$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767825 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300139203321 996 $aMethods of Algebraic Geometry in Control Theory: Part II$91923101 997 $aUNINA