Partially decentralized control of large scale systems with prescribed stability

This paper discusses the problem of assigning the eigenvalues of a multi-input linear large scale system (LSS) in such a way that a certain degree of decentralized state feedback controls is obtained. It is proven that for an n-order system with m independent inputs the problem is split into the following two sequential stages. Initially the n-m eigenvalues are assigned using an n-m order system. This assignment determines the non-square part of the state feedback gain-matrix. Next, an m-order system is used to assign the remaining m eigenvalues so that the square part of the state feedback gain-matrix takes on a diagonal form. Therefore, the state feedback gain-matrix leads to partially decentralized control schemes since each input is fed-back by a local state variable and n-m common state variables. For LSS, this means a drastic reduction of the measured states at each input, from n to n-m+l, without any risk on stability. Copyright (C) 1998 IFAC.