Characterization of decentralized fixed modes using inverse matrix factorization

This paper deals with issues pertaining to the assignment of closed loop eigenvalues under a decentralized control setting in the following way: 1. Characterization of decentralized fixed modes using inverse matrix factorization. This characterization differs from existing results in that it does not assume an a priori feedback structure and can therefore be used as a constructive test to determine a feasible decentralized structure (i.e. one with no unstable decentralized fixed modes). 2. Determination of a minimal decentralized feedback structure to minimize implementation complexity. 3. Application of the results to the stabilization of lightly damped systems. Furthermore, it is shown that if a plant does not have any co-located open-loop eigenvalues and transmission zeros, then at most min(r,m) feedback elements are required to shift all eigenvalues where r and m are, respectively, the number of outputs and the number of inputs.