Decentralized controllable subspace and unobservable subspace of large-scale systems

The concepts of decentralized controllable subspace and unobservable subspace are presented. The relations between them and their counterparts in centralized control were explored respectively. An approach similar to the geometric control theory in centralized control was adopted. The result shows that the decentralized controllable subspace and unobservable sub-space are the natural generalization of the controllable subspace and unobservable subspace to decentralized control respectively. Based on these concepts, some problem, such as stabilizing of large-scale systems by time-varying decentralized control, can be dealt with easily by a geometric approach.