State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

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

doi:10.1007/s11071-015-2162-6

Cited by 22 publications

(8 citation statements)

References 27 publications

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“…As in the proof of Theorem 1 and let σ ∈]0, δ[, then inequality (28) is verified. Now, the objective is to prove the uniform practical stability of (21).…”

Section: Practical Exponential Stabilitymentioning

confidence: 99%

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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“…As in the proof of Theorem 1 and let σ ∈]0, δ[, then inequality (28) is verified. Now, the objective is to prove the uniform practical stability of (21).…”

Section: Practical Exponential Stabilitymentioning

confidence: 99%

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

Echi

2019

Asian Journal of Control

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“…Observers are regarded as very important structures in control theory, with the fundamental task of reconstructing the states. Note that these estimators have been widely used in other advanced tasks, such as control problems [1][2][3]. For many decades, the observer-based state estimation problem has been extensively investigated for integer-order nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

State estimation for nonlinear conformable fractional‐order systems: A healthy operating case and a faulty operating case

Jmal¹,

Elloumi

Naifar³

et al. 2019

Asian Journal of Control

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The issue of estimating states for classical integer‐order nonlinear systems has been widely addressed in the literature. Yet, generalization of existing results to the fractional‐order framework represents a fertile area of research. Note that, recently, a new and advantageous type of fractional derivative, the conformable derivative, was defined. So far, the general query of designing observers for conformable fractional‐order systems has not been investigated. In addition, it has been proved in the literature that some important tools for stability analysis of fractional‐order systems are valid using the conformable derivative concept, but invalid using other fractional derivative concepts. Motivated by the cited facts, this paper presents a first‐state estimation scheme for fractional‐order systems under the conformable derivative concept. A healthy operating case and a faulty operating case are treated. In this paper, a version of Barbalat's lemma, which is invalid using the well‐known Caputo derivative, is exploited to prove the convergence of the estimation errors. In order to validate the theoretical results, a numerical example is studied in the simulation section.

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“…It should be noted that time delay may be, in some applications like communication lines, a source of instability and performance degradation [4]. Time delay system is therefore a very important class of processes whose stabilization [5] and optimization [6,7] have been of interest to many researchers.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

Bouafoura

Braïek

2019

Complexity

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The aim of this paper is to determine the optimal open loop solution and a nonlinear delay-dependent state feedback suboptimal control for a class of nonlinear polynomial time delay systems. The proposed method uses a hybrid of block pulse functions and Legendre polynomials as an orthogonal base for system’s states and input expansion. Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.

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State feedback control law for a class of nonlinear time-varying system under unknown time-varying delay

Cited by 22 publications

References 27 publications

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

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

State estimation for nonlinear conformable fractional‐order systems: A healthy operating case and a faulty operating case

Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

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