Robust input–output stabilization on ZZ for persistent signals

Robustness of feedback stabilization is studied for causal linear time-invariant input–output systems defined on the full time axis ZZ. The signal space setting used includes also certain unbounded signals. This study has been possible due to the use of two-operator plant models Ay=BuAy=Bu. This avoids the intrinsic difficulties of unbounded causal input–output plant mappings y=Guy=Gu on ZZ. The full time axis robust stabilization results obtained here are analogous to those on the semi-infinite time axis NN in the finite-dimensional case. However, there are certain important differences between the full time axis results and the semi-infinite time axis results for infinite-dimensional systems even when two-operator plant models are used.