Persistent excitation by deterministic signals in subspace MISO Hammerstein system identification

The persistent excitation issue is considered for MISO Hammerstein system identification using the subspace approach. A signal generator that provides deterministic persistently exciting (PE) sequences is developed. These are obtained by operating amplitude weighting and phase shifting on a discrete Dirac Comb signal of finite length. The proposed signal generation procedure presents quite interesting features e.g. the signals data samples are deterministic, weakly constrained, and their size do not need to be too large. Theoretically, the signal generator design relies on a technical lemma establishing the PE property for the considered identified systems. The effectiveness of the proposed class of exciting sequences is confirmed by simulation.