Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Linear Systems

In this paper, the normal Luenberger function observer design for second-order linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.