On Observer Design for a Class of Nonlinear Systems Including Unknown Time-Delay

Naifar, Omar; Makhlouf, Abdellatif Ben; Hammami, Mohamed; Ouali, A.

doi:10.1007/s00009-015-0659-3

Cited by 19 publications

(32 citation statements)

References 27 publications

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“…By the following theorem, the Mittag Leffler stability of the observer (6), with the one sided Lipschitz condition (8), is ensured. …”

Section: Observer Design For One-sided Lipschitz and Quasi-one-simentioning

confidence: 99%

“…Observer design for Lipschitz systems was first considered by Thau [4]. Recently, two studies have attempted to solve the problem of observer design for Lipschitz systems with time delay: in [7], the authors have tackled the Lipschitz discrete-time systems, while in [8], they tackled the Lipschitz continuous-time systems with unknown time delay. More recently, Abbazadeh and Marquez [6] developed a robust H∞ observer for sampled-data Lipschitz nonlinear systems with exact and Euler approximate models.…”

Section: Introductionmentioning

confidence: 99%

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On Observer Design for Nonlinear Caputo Fractional‐Order Systems

Jmal

Naifar

Makhlouf

et al. 2017

Asian Journal of Control

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The observer design problem for integer-order systems has been the subject of several studies. However, much less interest has been given to the more general fractional-order systems, where the fractional-order derivative is between 0 and 1. In this paper, a particular form of observers for integer-order Lipschitz, one-sided Lipschitz and quasi-one-sided Lipschitz systems, is extended to the fractional-order calculus. Then, the obtained states estimates are used for an eventual feedback control, and the separation principle is tackled. The effectiveness of the proposed scheme is shown through simulation for two numerical examples.

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“…By the following theorem, the Mittag Leffler stability of the observer (6), with the one sided Lipschitz condition (8), is ensured. …”

Section: Observer Design For One-sided Lipschitz and Quasi-one-simentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Observer Design for Nonlinear Caputo Fractional‐Order Systems

Jmal

Naifar

Makhlouf

et al. 2017

Asian Journal of Control

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“…In [26], it is shown that observer design for a class of nonlinear time delay systems is solved by using linear matrix inequality. In [11], some sufficient conditions for practical uniform stability of a class of uncertain time-varying systems with a bounded time-varying state delay were provided using the Lyapunov stability theory.[4] and [9] show that state and output feedback controllers of time-delay systems, written in a triangular linear growth condition are reached under delay independent conditions and under delay dependent conditions respectively.The observer design problem for nonlinear systems satisfying a Lipschitz continuity condition has been a topic of numerous papers, such as for nonlinear free-delay systems [1,2,27,25], for nonlinear systems with unknown, time-varying [19,14,12]. A reduced-order observer design method is presented in [27] for a class of Lipschitz nonlinear continuous-time systems without time delays which extend the results in [25].However, in practice, dynamics, measurement, noises or disturbances often prevent the error signals from tending to the origin.…”

mentioning

confidence: 99%

“…For this reason, the property is referred to as practical stability which is more suitable for nonlinear free-delay systems ( see [5,7]) and for nonlinear systems with time-delay ( see [10,14,19,24]). Under unknown, bounded timedelay, an observer design for a class of nonlinear system is presented in [19]. [10] concluded that a class of nonlinear time delay systems is conformed due to some assumptions and the time varying delay bounded the practical exponential stability.…”

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confidence: 99%

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Observer design and practical stability of nonlinear systems under unknown time‐delay

Echi

2019

Asian Journal of Control

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In the present paper, we study observer design and we establish some sufficient conditions for practical exponential stability for a class of time-delay nonlinear systems written in triangular form. In case of delay, the exponential convergence of the observer was confirmed. Based on the Lyapunov-Krasovskii functionals, the practical stability of the proposed observer is achieved. Finally, a physical model and simulation findings show the feasibility of the suggested strategy.Mathematics Subject Classification. 93C10, 93D15, 93D20.Time-delay systems are one of the basic mathematical models of real phenomena such as nuclear reactors, chemical engineering systems, biological systems [16], and population dynamics models [18]. The analysis of systems without delays is generally simple as compared to nonlinear systems under time delays. However, there are a number of problems relating to nonlinear observer for time delay system. In particular, a problem of theoretical and practical importance is the design of observer-based for time-delay systems. In literature, a separation principle, for nonlinear free-delay systems, using high gain observers is provided in [1] and [2].Much attention has been paid to solve such a problem and many observer designs for time-delay nonlinear systems approaches have been used. In [26], it is shown that observer design for a class of nonlinear time delay systems is solved by using linear matrix inequality. In [11], some sufficient conditions for practical uniform stability of a class of uncertain time-varying systems with a bounded time-varying state delay were provided using the Lyapunov stability theory.[4] and [9] show that state and output feedback controllers of time-delay systems, written in a triangular linear growth condition are reached under delay independent conditions and under delay dependent conditions respectively.The observer design problem for nonlinear systems satisfying a Lipschitz continuity condition has been a topic of numerous papers, such as for nonlinear free-delay systems [1,2,27,25], for nonlinear systems with unknown, time-varying [19,14,12]. A reduced-order observer design method is presented in [27] for a class of Lipschitz nonlinear continuous-time systems without time delays which extend the results in [25].However, in practice, dynamics, measurement, noises or disturbances often prevent the error signals from tending to the origin. Thus, the origin is not a point of equilibrium of the system. An additive term on the right-hand side of the nonlinear system is used to present the uncertainties systems. For this reason, the property is referred to as practical stability which is more suitable for nonlinear free-delay systems ( see [5,7]) and for nonlinear systems with time-delay ( see [10,14,19,24]). Under unknown, bounded timedelay, an observer design for a class of nonlinear system is presented in [19]. [10] concluded that a class of nonlinear time delay systems is conformed due to some assumptions and the time varying delay bounded the practical exponentia...

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