Fault tolerant control: a simultaneous stabilization result

This note discusses the problem of designing fault tolerant compensators that stabilize a given system both in the nominal situation, as well as in the situation where one of the sensors or one of the actuators has failed. It is shown that such compensators always exist, provided that the system is detectable from each output and that it is stabilizable. The proof of this result is constructive, and a worked example shows how to design a fault tolerant compensator for a simple, yet challenging system. A family of second order systems is described that requires fault tolerant compensators of arbitrarily high order.