Zeros and the Output-Zeroing Problem -- A General Solution to the Output-Zeroing Problem -- The Moore-Penrose Inverse of the First Markov Parameter -- Singular Value Decomposition of the First Markov Parameter -- Output-Nulling Subspaces in Strictly Proper Systems -- Output-Nulling Subspaces in Proper Systems -- Singular Systems.

A state space approach to the analysis of zeros of MIMO LTI discrete-time systems is presented. The basic mathematical tools used in this analysis are the Moore-Penrose pseudoinverse and singular value decomposition of the first nonzero Markov parameter of a system. The book starts with definition of invariant zeros and goes as far as a general characterization of output-zeroing inputs and the corresponding solutions, explicit formulas for maximal output-nulling invariant subspaces and for the zero dynamics. The objective of this book is to render the reader familiar with a certain method of analysis of multivariable zeros (which goes beyond the classical approach) and related problems. The minimal mathematical background that is required from the reader is a working knowledge of linear algebra and difference equations. The reader should be familiar with the basic concepts of linear system theory.