ODE observers for DAE systems. (29th August 2018)

• Record Type: Journal Article
• Authors: Berger, Thomas; Reis, Timo
• Is Part Of: IMA journal of mathematical control and information. Volume 36:Number 4(2019)
• Page Start: 1375
• Page End: 1393
• Publication Date: 2018-08-29
• Subjects: differential-algebraic equations -- observers -- controllability -- observability -- Kalman decomposition; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dny032
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: We consider linear time-invariant differential-algebraic systems which are not necessarily regular. The following question is addressed: when does an (asymptotic) observer which is realized by an ordinary differential equation (ODE) system exist? In our main result we characterize the existence of such observers by means of a simple criterion on the system matrices. To be specific, we show that an ODE observer exists if, and only if, the completely controllable part of the system is impulse observable. Extending the observer design from earlier works we provide a procedure for the construction of (asymptotic) ODE observers.