The purpose of this research monograph is to utilize algebraic and systems theory for the structure analysis and design of multivariable control systems described by state-space representations and matrix fraction descriptions. A unified approach characterizing the dynamics of a system through the formulation of the characteristic -matrix of the system is presented. The latent structures, solvents, divisors, and spectral factors of the non-singular characteristic -matrix and their relationships with the respesctive counterparts of the state-space representations are explored. Applications in model reduction, pole assignment design, modal control design for multivariable systems, parallel realizations and cascade realizations of multiport networks are illustrated. Computational algorithms and illustrative numerical examples are presented throughout the monograph. The reader is assumed to have a graduate level background in modern control theory.