Title: Unknown input observer for linear singular systems with variable delay: the continuous and the discrete time cases

Authors: Fatma Hamzaoui; Malek Khadhraoui; Hassani Messaoud

Addresses: Research Laboratory LARATSI, National Engineering School of Monastir (ENIM), University of Monastir, Tunisia ' Research Laboratory LARATSI, National Engineering School of Monastir (ENIM), University of Monastir, Tunisia ' Research Laboratory LARATSI, National Engineering School of Monastir (ENIM), University of Monastir, Tunisia

Abstract: In this paper, we propose a new approach to design a functional observer for linear singular systems with unknown inputs. Variable-Time delay is present in both state and input vectors. The proposed observer is developed in time and frequency domains. The time domain observer design is obtained for both continuous and discrete time systems. The procedure design is based on the unbiasedness of the estimation error dynamic of the observer using Lyapunov functional. The problem is solved by means of linear matrix inequalities to find the optimal gain implemented in the functional observer design. Frequency domain procedure is derived from time domain results, where we propose a suitable co-prime matrix fractions description. The main interest is that the proposed algorithm estimates both a functional state and the unknown input independently from the considered delay in time and frequency domains. The proposed observer proves its effectiveness on a given numerical example.

Keywords: continuous and discrete time cases; time and frequency domains; unknown additional inputs; functional observers; variable delay; MFD; linear matrix inequalities; LMI.

DOI: 10.1504/IJMIC.2022.127517

International Journal of Modelling, Identification and Control, 2022 Vol.41 No.3, pp.193 - 205

Received: 13 Sep 2021
Accepted: 09 Dec 2021
Published online: 07 Dec 2022 *

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