Canonical realization of observers wilth arbitrarily assigned poles for linear functions of the state

This paper shows that an observer Σ_ob(Â, [Bcirc], Ĉ, [Dcirc], ˆJ) for a linear function Kx of the state of a time-invariant linear system Σ(A., B, C) is characterized by a new system Σ_OB(Â, [Bcirc], Ĉ, [Dcirc]) with the initial state Ĵ which receives Markov parameters (CA^tB)_{t =0, … +μ−1}as the input and gives (KA_tB)_{t=, v+μ−1}as the output, where v is the controllability index of (A, B) and;μ is the observability index of (Â, Ĉ), It admits that the observer is constructed by a realization of σ_OB(Â, [Bcirc], Ĉ, [Dcirc]) from the input-output data and a determination of the initial state Ĵ. An algorithm is presented to construct the lower order observer with arbitrarihy assigned poles in a canonical form.