On the notion of strong stabilizability

A system is called strongly stabilizable (SS) if it can be stabilized using a stable controller. Observer state feedback can be used to design a controller of the same order as the system, but the designs may lead to unstable controllers. The implementation of an unstable controller should be done with care and with a well-designed safety net. One implementation could use a stable observer fed with actual input in addition to the measured output. Several examples are discussed, and how unstable controllers might be required for good closed-loop performance, even if they are not required for stability is shown