Unknown Input Observer-Based Design for a Class of Nonlinear System with Time-Variable Delay
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Unknown Input Observer-Based Design for a Class of Nonlinear System with Time-Variable Delay Ikram Triki1
· Ramzi Ben Massaoud2 · Faouzi Bouani1
Received: 14 February 2019 / Revised: 6 February 2020 / Accepted: 25 April 2020 © Brazilian Society for Automatics–SBA 2020
Abstract This paper addresses the problem of state estimation for nonlinear delay systems by proposing an unknown inputs observer. The observer design is based on using Taylor’s first-order development. The stability study has been proven using a modified Lyapunov–Krasovskii functional without reference to a linear matrix inequality. For the validation of the proposed approach, three examples are proposed. The first one is about comparative simulation, the second one treats the chaotic time-delay system and the final example considered the time-delay system with measurement noise. Keywords Nonlinear observer · Unknown input · Nonlinear time-delay system · Stability · State estimation
1 Introduction Over the last decades, many research activities have focused on the issue of observing the state of nonlinear time-delay systems (Karimi and Chadli 2013; Zuo et al. 2017). This is due to the major role that estimation plays in the synthesis of the control law and fault detection (Yan et al. 2017; Chaves et al. 2019). Time-delay systems exist in many fields such as mechanical systems, networks communication, robotized teleoperation, mobile telecommunication (Chiasson and Loiseau 2007) and synchronization in communication systems (Jafari et al. 2016). Different approaches have been developed to treat nonlinear time-delayed systems with perturbation from the extended Kalman filter EKE (Raff and Allgower 2006; Hugues-Salas and Shore 2010). In the last years, in the case of systems presenting Lipschitz nonlinearities the sliding mode is taken into account (Koshkouei and Burnham 2009). Moreover, there was significant research focused on the estimation of the state of dynamic systems with unknown
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Ikram Triki [email protected]
1
Université de Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, LR11ES20 Laboratoire d’Analyse, de Conception et de Commande des Systèmes, Tunis, Tunisie
2
Laboratoire de Nanomateriaux et des Systèmes pour les Ènergies Renouvelables, Centre de Recherches et des Technologies de l’Energie, BP. 95, Hammam Lif 2050, Tunisia
input. An unknown input observer is an observer that requires no knowledge of the unknown entry. One of the original ideas related to UIO for Lipschitz class is given in Yaz and Azemi (1998) in which fault detection has been made by resolving LMI and LME. Also, there is other interesting ideas in continuous case for the state-delayed systems estimation (Chakrabarty et al. 2018; Hassan et al. 2019; You et al. 2016; Gu and Yang 2010). Since that several engineering fields need to be treated in the discrete case. The UIO was extended to be adapted to all technical features. Many research works have focused on this subject (Lin and Gao 2015; Benkouider et al. 2016). Also, a great attention was given to th
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