On the order reduction of linear function observers

This note analyzes a new algorithm presented in [1] for designing a linear function observer with a minimum number of arbitrary poles. It shows that the maximum order of the observer of [1] is\nu + ... + \nu_{p} - pforp \leq qandn - qforp \geq q, instead ofp(\nu_{1} - 1)as suggested in [1], where\nu{i}, i = 1top, are the descending ordered observability indexes of system (A, C) andn,p, andqare the order of the system, the number of the functions, and the number of the system outputs, respectively. This note also shows the significance of this result. For presentational purposes, only a special case of [1] is considered here. However, the technical properties as proved in this note are general.