Functional Detectability and Asymptotic Functional Observer Design

Mohamed Darouach, Tyrone Fernando

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


he objective of this paper is to present a new solution to the functional observer design problem. First a new definition of the functional detectability is given, then some algebraic conditions for linear multivariable systems to be functionally detactable are presented. They generalize the existing conditions and coincide with those existing for the detectability and the asymptotic Luenberger observer design of the full and reduced-order cases. Then necessary and sufficient conditions for the existence of an asymptotic functional observer are given and complete those existing in the literature. The connection with the Sylvester equation and its solution are also given. The functional observer parameters are obtained from this Sylvester equation and functional detectability. Necessary and sufficient conditions for stability of the presented functional observers are given in the form of matrix inequalities based on two approaches: the first approach is based on the stability analysis of the solution of the Sylvester equation, and the second approach is based on the Frobenius canonical form and its spectrum, which leads to a static output feedback (SOF) formulation. Necessary and

Original languageEnglish
Pages (from-to)975-990
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number2
Early online date16 Feb 2022
Publication statusPublished - 1 Feb 2023


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