This paper is concerned with the controllability of symmetric systems. In particular, we aim to give a lower bound for the number of functioning modules needed to keep the entire symmetric system controllable. Our concern is the characteristics derived of the symmetry of the systems, i.e., the uncontrollability caused solely by the symmetric structures, and not by the numerical information nor by the sparsity of the connections among the modules. If all the modules are connected, only one functioning module would suffice to keep the controllability. For symmetric systems, however, it is shown that we need more than one functioning module to keep the entire system controllable. We treat systems of general symmetry and show the lower bound based on group representation theory.
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