Title: Proportional integral observer using disturbance attenuation strategy for discrete-time linear singularly perturbed system

Authors: Ltifi Marwa; Bahri Nesrine; Ltaief Majda

Addresses: Research Laboratory of Numerical Control of Industrial Processes (CONPRI), National Engineering School of Gabes, University of Gabes, Street Omar Ibn Khattab, 6029, Gabes, Tunisia ' Research Laboratory of Numerical Control of Industrial Processes (CONPRI), National Engineering School of Gabes, University of Gabes, Street Omar Ibn Khattab, 6029, Gabes, Tunisia ' Research Laboratory of Numerical Control of Industrial Processes (CONPRI), National Engineering School of Gabes, University of Gabes, Street Omar Ibn Khattab, 6029, Gabes, Tunisia

Abstract: This paper deals with the observability bound problem of a discrete-time linear singularly perturbed system (DTLSPS) subject to L₂ disturbance and L₂ noise. A proper PI observer, known by its robustness, is devised for state estimation, ensuring that the observation error is asymptotically stable and satisfies the H_∞ performance constraint for a proper bound of the singular perturbation parameter based on a quadratic Lyapunov function and the H_∞ norm. In order to design this observer, sufficient conditions expressed in terms of linear matrix inequalities (LMIs) are developed to ensure the robust stability bound of the considered system. This task is also achieved using a quadratic Lyapunov function and the H_∞ norm. Then, using the outcomes of these two tasks, the observability bound of the system is determined. Two simulation examples are then given to validate the proposed strategy.

Keywords: time linear singularly perturbed system; noise; disturbance; robust stability bound; observability bound; proportional integral observer.

DOI: 10.1504/IJMIC.2023.133440

International Journal of Modelling, Identification and Control, 2023 Vol.43 No.4, pp.312 - 324

Received: 17 May 2022
Received in revised form: 18 Oct 2022
Accepted: 29 Nov 2022
Published online: 15 Sep 2023 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article