Fatma Hamzaoui

This paper introduces an innovative and efficient method for estimating the state functional of linear discrete-time systems with delays that are subject to actuator and sensor faults, which are represented by unknown inputs. The aim of this paper is twice: first, to design a robust observer that accurately and stably estimates the considered state functional; and second, to reconstruct the inputs responsible for the occurrence of faults. We develop the observer dynamics using Lyapunov–Krasovskii theory. This theory enables us to construct an appropriate functional that ensures convergence, stability, and robustness of the estimation error despite the presence of delays. The proposed strategy provides a systematic framework for fault estimation and compensation in delayed discrete systems. To evaluate the method’s validity and efficiency, we apply it to a disinfection tunnel system benchmark. The simulation results clearly demonstrate the observer’s satisfactory performance and accurate estimation of the state functional and unknown fault inputs.

This paper proposes a functional observer for a bilinear singular systems with constant time delay present in both state and known input vectors. The considered system has transformed to an updated form in order to estimate both a state vector and an unknown inputs functional vector independently from the considered time delay. The necessary conditions for the existence of the functional observer are formulated. The proposed observer design procedure is based on the Lyapunov–Krasovskii theory. Numerical example is given to prove the new approach.