Simultaneous stabilization via linear state feedback control

The problem of simultaneously stabilizing a finite collection of plants via a single compensator utilizing full state information is considered. This work exploits a recent result due to B.R. Barmish and K.H. Wei (1985), which states that a finite collection of plants can be simultaneously stabilized if all the plants are minimum phase and have the same sign high-frequency gain. In contrast to the dynamic output feedback controller used in a previous work, it is assumed that the complete state can be measured, and a (static) linear state feedback control law is sought. Sufficient conditions for such full state gains to exist are given, and it is shown by several examples how stabilizing compensators can be designed