Global exponential stabilisation of a class of nonlinear time-delay systems

Benabdallah, Amel; Echi, Nadhem

doi:10.1080/00207721.2015.1135356

Cited by 16 publications

(14 citation statements)

References 18 publications

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“…A strong practical observer for system (2) is a family of auxiliary dynamic systems written asẋ = G ε (t,x(t),x(t − τ ), y(t)) such that for all t ≥ 0 Remark 2.3. When ρ(ε) = 0, in this case the origin is an equilibrium point, then we point the classical definition of the exponential stability (see [5,32]). Notation 1.…”

Section: System Description and Basic Resultsmentioning

confidence: 94%

“…Under a Lyapunov-Krasovskii functional, suitable choice, [24] derived a control scheme to design an adaptive control to stabilize the nonlinear time-delay systems. These stability findings obtained for delayed systems can be generally classified into two main types, namely delay independent [4,5,12,31] and delay dependent [11,15]. [16] has suggested the problem of observer for a class of nonlinear delay systems.…”

Section: Introductionmentioning

confidence: 99%

“…Much attention has been paid to solving the problem of exponential stability because it is an important index to obtain the convergence rates of prescribed time-delay systems. Therefore, exponential stability of systems with delays has been the interest of researchers and the subject of numerous papers and monographs [5,9,11,19,26,29,31]. Based on the Lyapunov method, [26] derived a linear matrix inequality.…”

Section: Introductionmentioning

confidence: 99%

“…In [10] sufficient conditions are provided to prove the practical stability for a class of nonlinear delay systems satisfying some relaxed triangular-type condition. According to the Lyapunov-Krasovskii functional, the problem of global exponential stability of a class of nonlinear time-delay systems written in triangular form that satisfies a linear growth condition is achieved by [5]. [29] derives sufficient conditions expressed in terms of linear matrix inequalities (LMIs) for exponential stability of linear time-delay systems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Observer based control for strong practical stabilization of a class of uncertain time delay systems

Echi¹,

Benabdallah²

2020

Kybernetika

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Section: System Description and Basic Resultsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Observer based control for strong practical stabilization of a class of uncertain time delay systems

Echi¹,

Benabdallah²

2020

Kybernetika

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“…In this paper we investigate the stabilisation problem for a class of uncertain time delay fractional differential systems with a nominal part written in triangular form. Motivated by similar approaches to time-delay first-order differential systems [3,9] as well as [15], we design a state feedback controller to stabilise the origin of the system and give sufficient conditions for the stabilisation of nonlinear systems with time-varying delays as linear matrix inequalities.…”

Section: Introductionmentioning

confidence: 99%

A Separation Principle for the Stabilisation of a Class of Fractional Order Time Delay Nonlinear Systems

Echi

Basdouri

Benali

2018

Bull. Aust. Math. Soc.

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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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Global exponential stabilisation of a class of nonlinear time-delay systems

Cited by 16 publications

References 18 publications

Observer based control for strong practical stabilization of a class of uncertain time delay systems

Observer based control for strong practical stabilization of a class of uncertain time delay systems

A Separation Principle for the Stabilisation of a Class of Fractional Order Time Delay Nonlinear Systems

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

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