Abstract This paper studies the effects of decentralized feedback on the closed-loop properties of jointly controllable, jointly observable k-channel linear systems. Channel interactions within such systems are described by means of suitably defined directed graphs. The concept of a complete system is introduced and completeness is shown to be a generic property of systems with strongly connected graphs. Complete systems prove to be precisely those systems which can be made both controllable and observable through a single channel by applying nondynamic decentralized feedback to all channels. Explicit conditions are derived for determining when the closed-loop spectrum of a k-channel linear system can be freely assigned or stabilized with decentralized control. These conditions are shown to hold generically for systems with strongly connected graphs.