In this work, the decentralized stabilization and decentralized servomechanism problem for descriptor systems is considered. A descriptor system is one characterized by the existence of algebraic constraints on the plant state variables. Such constraints may translate into undesirable impulsive behavior, a property not found in conventional, proper, state space systems. Conditions are therefore investigated to determine if a system can be made "impulse-free" by suitable feedback action, and in this case the conditions are expressed in terms of the so-called decentralized impulsive fixed modes of the system. The notions of transmission zeros and decentralized fixed modes are defined for the class of descriptor systems and it is shown that they play a central role in determining the solvability of the decentralized robust servomechanism problem for descriptor systems. Two applications, tuning regulator design and sequential synthesis, are also addressed in this work.