This paper presents a decentralized observation scheme for linear time‐invariant interconnected systems where the interaction is characterized by the subsystem outputs. Using the conventional optimal technique guaranteeing a prescribed degree of stability, the nominal observer gains are first calculated with respect to the decoupled system and then are multiplied by appropriate factors to adapt the interaction among the subsystems. This subsystem‐based approach not only can yield at least a prescribed convergent rate of the global reconstruction error system but also can effectively reduce the burden of computations and simplify the design procedures. Computer simulations of an example of a sixth‐order interconnected system containing three subsystems are conducted.