A Note on Functional Observability

Abstract

In this note, we propose an alternative to characterize the functional observability for linear systems. The main feature is that we obtain a necessary and sufficient condition for the existence of a stable multi-functional observer of a time-invariant linear system. The proof of this condition is constructive and it leads to design a stable observer via a new procedure, neither based on the solution of a Sylvester equation nor on the use of canonical state space forms.

Design Procedure for Linear Unknown Input Functional Observers

“…From the use of successive derivatives of state functionals, an usual realization method leads to obtain the observer. It can be remarked that the presented results extend the results in [28] in the case where unknown inputs are present. Finally, an example illustrates the procedure in Section V and points out the advantage of the proposed design regarding the previous ones.…”

“…Remark 10. From the expressions (20) for the matrices Φ i and the relationship G = T B (6), it can be deduced, as it has been indicated for LFO in [28], that…”

“…To design a functional observer, the triplet (A, C, L) has to be functionally observable [28], i.e. :…”

“…A realization of the input-output differential Equation (19) [24], [28], [36] leads to the observer:…”

Minimal Order Linear Functional Observers Design for Multicell Series Converter

“…, s}, s is the number of linear functional to observe and n is the order of the system. This observer is developed to estimate the linear function v i (t) such as: The following assumptions [23] [19] [20] have to be verified to ensure that a functional observer exists:…”