Cooperative interconnected systems: Eigenvalue assignment

The concept of cooperation have been addressed in diverse areas in large scale systems (LSS) studies under different nomenclature. For a historical-phenomenological survey of the roots of this concept we refer to [1][2]. This perception of system and control fitted very well the needs of utilizing it as an efficient powerful design tool in an important area of LSS studies that have not received the adequate attention, namely, eigenvalue assignment. There is a relative sparse literature on such untractable problem. An algorithm for stabilizing LSS through cooperation was presented in [3][4]. The present paper extends the applicational area of the concept of cooperation. The global eigenvalue assignment problem is decomposed to several similar subproblems. Each is solved independently through local decisions on subsystems- coordinator level. Subsystems cooperate to modify local decisions in order to achieve the prescribed spectrum. In contrast to previous work, global problem reduction and precise eigenvalue assignment is achieved without any sacrifice.