This text is the first comprehensive treatment of structural decompositions of various types of linear systems, including autonomous, unforced or unsensed, strictly proper, non-strictly proper, and descriptor or singular systems. Structural properties play an important role in the understanding of linear systems and also provide insight to facilitate the solution of control problems related to stabilization, disturbance decoupling, robust and optimal control. Applications can be extended to industrial process control, aircraft and ship control, process automation control, and many other types of engineering systems. The authors employ a unique structural decomposition approach to break down an overall system into various subsystems, each with distinct features. The simplicity of these subsystems and their interconnections lead to deep insight about the design of feedback control systems for desired closed-loop performance, stability, and robustness.