On the computation of zeros in systems identified from output signals

摘要

The paper presents an extension of the standard state space approach to compute transfer function zeros to systems identified without deterministic information on the input.The extension is grounded on the fact that the observed output could have been generated by collocated inputs and that the span of the input to state matrix B associated with this condition is constrained by the {A,C} duplet of the stochastic identification.Two variants of the approach are presented,one which uses a minimum number of constraints from A and C and one that uses the maximum possible number.The advantage of the first option is conceptual simplicity but the disadvantage is that the solution is not independent of the state-space basis.It is shown,however,that the basis dependency can be removed by averaging.In the second implementation the solution is independent of the realization basis.The two implementations are found to provide similar accuracy in the numerical examples considered.