Methods of Algebraic Geometry in Control Theory: Part II

• 1 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.

"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