Subspaces invariance constraints in Large Scale Systems

Modeling and control of Large Scale Systems (LSS) have been deeply investigated in the last decades. Most methodologies used to study LSS, both for model reduction and control design, can be interpreted using geometric tools. In this paper we address the role of subspaces invariance in such methodologies and stress the limitations imposed by the invariance requirement. Moreover we investigate how the notions of Phi-related vector fields and control systems seem to be the key ingredient for removing such constraints in control design.