This paper present analgebraictheory for linear time-invariant multi-input multi-output systems with two-input two-output plant and compensator, using the factorization approach. This system configuration considered by Doyle and Nett is most general in that any interconnection of two systems can be represented in terms of this scheme. Other system configurations encountered in compensator design problems are special cases of this system configuration. The analysis and synthesis applies to continuous-time as well as discrete-time systems, and to lumped as well as distributed systems, since the algebraic setting is completely general. The compensator parametrization has four degrees of freedom. The paper is self-contained and is tutorial in the sense that it develops the main results of Nett without introducing the concept of containment.