An application of Lie groups in distributed control networks

Here we introduce a class of linear operators called recursive orthogonal transforms (ROTs) that allow a natural implementation on a distributed control network. We derive conditions under which ROTs can be used to represent SO(n) for n¿4. We propose a paradigm for distributed feedback control based on plant matrix diagonalization. To nd an ROT suitable for this task, we derive a gradient ow on the appropriate underlying Lie group. A numerical example is presented. c © 2001 Elsevier Science B.V. All rights reserved.