Abstract
This paper considers the dynamical hierarchical control systems (DHCS), which are formed by the designed dynamical cooperation controller (DCC) and the hierarchical control laws (HCL) and large scale systems (LSS). When the state of LSS is available, we prove that there exist DCC and HCL such that DHCS have any pre-assigned spectrum if and only if the LSS is controllable. In order to deal with the minimal order DCC, we define the new concepts: decentralized state feedback cycle index of LSS, geometric multiplicity of decentralized fixed made. And their computational methods are also given. In addition, a concept of decentralized state feedback variable polynomial of LSS is introduced, and its some properties are also given. It is proved that the decen- tralized state (output) cycle index of the LSS is equal to 1 when the LSS has no decentralized fixed mode, or the maximum of geometric multiplicities of decentralized fixed modes otherwise. And the minimal order of DCC is equal to the decentralized state feedback cycle index. Finally, a synthesis method for DCC and HCL is given.
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