Methods of algebraic geometry in control theory: Part II. Multivariable linear systems and projective algebraic geometry (Q1667426)

The book is a continuation of Part I [Zbl 1397.93052], which dealt with linear SISO systems using affine algebraic geometry. Part II extends these results to MIMO systems using projective algebraic geometry. Starting from Chapter 1, the work addresses the use of affine algebraic geometry from SISO systems to SIMO or MISO systems. Then, MIMO systems are considered, for which projective algebraic geometry is used to study them. System representations are considered first, and then the theory of projective algebraic geometry is studied, starting from introductory material and building up to more advanced concepts. Problems like state space realizations, controllability, observability, equivalence, the Laurent isomorphism theorem, the geometric quotient theorem, state and output feedback are presented. Since this work builds up from the results of Part I, it is essential that the interested readers have a background on algebraic geometry, and are also familiar with the theory presented in the first part. Yet, there is enough introductory material and appendices that can be used to refresh the needed background, so that the reader does not have to go back and forth between volumes. Thus, this volume is self contained. In addition, combined with Part I, it gives a thorough presentation of the field of control theory and algebraic geometry.