Symmetric failures in symmetric control systems Original Research Article

This paper discusses the fault-tolerance of symmetric systems with respect to controllability, which is a fundamental characteristic of control systems. In particular, we reveal the underlying mathematical mechanism of the loss of controllability for symmetric systems induced by failures. Based on the decomposition of the symmetric systems into subsystems under the symmetry, the controllability of the entire system can be discussed by checking that of each subsystem. The analysis of the fault-tolerance in this paper is an extension of this idea with the aid of the chain-adapted transformation matrix for the decomposition. The result is shown as a necessary condition for symmetric systems to retain the controllability despite some symmetric failures. We also discuss sufficient conditions.