Controllability of Hierarchical Systems with Direct Product Symmetry

This paper deals with symmetric control systems consisting of some modules with local internal symmetries. The symmetry of the whole system can be described with a direct product G×L of the groups G for global symmetry and L for local symmetry. As a characteristic determined from the two symmetries, we focus on the loss of controllability in the systems by certain symmetric failures and clarify that the conditions for the loss of controllability are given for each level of symmetry separately.