FIR stabilization in discrete one-sided model-matching problems

This note studies stabilization problems arising in discrete estimation (or preview tracking) problems when unstable exosystems are used to impose steady-state behavior constraints. The main theme is stabilizability conditions under FIR (finite impulse response) constraints. Necessary and sufficient stabilizability conditions are derived and all solutions are parametrized. Unlike the continuous-time case, where the problem is solvable under the standard detectability condition, stabilizability in the discrete-time case depends on the length of the impulse response and, sometimes, also on the smoothing lag (length of preview).