Decentralized control and periodic feedback

The decentralized stabilization problem for linear, discrete-time, periodically time-varying plants using periodic controllers is considered. The main tool used is the technique of lifting a periodic system to a time-invariant one via extensions of the input and output spaces. It is shown that a periodically time-varying system of fundamental period N can be stabilized by a decentralized periodic controller if and only if: 1) the system is stabilizable and detectable, and 2) the N-lifting of each complementary subsystem of identically zero input-output map is free of unstable input-output decoupling zeros. In the special case of N=1, this yields and clarifies all the major existing results on decentralized stabilization of time-invariant plants by periodically time-varying controllers