On the Order Reduction of Linear Functional Observers

This paper analyzes a new algorithm presented in [1] for designing a linear functional observer with arbitrary eigenvalues. It proves that the order of the observer in [1] is a reduction (depending on the problem) of a maximum order m=(¿l+...+¿p - p), where ¿i, i=l,...,p are the descending ordered observability indices of the system (A, C) and p is the number of the functionals. Therefore, the design algorithm in [1] is general for all cases in the design of both the functional observers as well as the state observers which can be regarded now as a special case of the functional observer.