Feasible Parameter Set for Bilinear Systems from Records with Bounded Output Errors

Parameter bounding is a well-founded alternative to classical parameter estimation methods when either statistical hypotheses on the errors are not met or uncertainties are no longer random variables but deterministic ones (e.g. systematic, round-off, truncation errors). So far, many efforts have been devoted to the problem of parameter bounding in linear systems, where exact parameter uncertainty intervals can be computed. Instead, only partial results have been found for nonlinear parametrization, namely, either upper or lower bounds on parameters uncertainties can be evaluated. In this paper, parameter bounds for bilinear systems with bounded output errors are derived, based on a linear input-output model and previous results of the author. Two approaches are outlined: the bounded errors-in-variables and the bounded equation error, which lead, respectively, to exact parameter uncertainty intervals and approximated ones.