Symmetric failures in symmetric control systems (Q1590654)

Fault-tolerance with respect to controllability of symmetric control systems is studied. Controllability is considered as a system characteristic to be retained despite failures in some control channels. The main result is a necessary condition for retaining controllability despite a symmetric failure. As the symmetry of a control system \((A,B)\) is associated with a finite group \(G\) and the symmetric failure with a subgroup \(H\) of \(G\), the condition is obtained and stated using standard group representation theory. A case in which this necessary condition is also sufficient is identified. Related sufficient conditions are also discussed.