An algebraic approach to the decentralized stabilization problem is considered in the framework of linear time-invariant hereditary systems. The problem considered is to determine conditions under which a stabilizable linear hereditary system can be made stabilizable from the input and output variables of a given control channel by static feedback applied to the other control channels. Then the observer-controller or the dynamic compensation scheme can be employed for this control channel in a standard way to make the closed-loop system stable. Necessary and sufficient conditions for the existence of stabilizing decentralized feedback controllers are presented and proved by using the fact that the number of unstable eigenvalues of a certain linear hereditary system is finite.
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