Observer‐Based H∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Zhao, Zhanshan; Du, Yanan; Zhang, Jing; Sun, Liankun

doi:10.1002/asjc.1783

Cited by 13 publications

(22 citation statements)

References 27 publications

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“…A tenth of researchers has studied the design problem of the observer for example in [15,27,30,31] and references therein. For nonlinear systems having triangular structures, the global asymptotic stability is proved using a high‐gain parameterized linear controller in [27].…”

Section: Resultsmentioning

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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Section: Resultsmentioning

confidence: 99%

“…[15] presented observer design for a class of nonlinear system with bounded time‐varying delay. Recently, based on the Lyapunov method and Lyapunov stability theory [31] derived a linear matrix inequality criterion to design an observer‐based controller to stabilize the delay system.…”

Section: Resultsmentioning

confidence: 99%

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

Echi

2019

Asian Journal of Control

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“…the regulated output to within a prescribed level. [13][14][15][16][17][18][19] The passivity theory was firstly proposed in circuit analysis. Passivity theory is a promising method to attain the internal stability of systems under consideration.…”

Section: Introductionmentioning

confidence: 99%

“…In the past, H ∞ performance criterion was usually used to reduce the effect of the disturbance input on the regulated output to within a prescribed level 13–19 . The passivity theory was firstly proposed in circuit analysis.…”

Section: Introductionmentioning

confidence: 99%

Mixed performance analysis of continuous switched systems with time‐varying random delay

Lien

Chang

2020

Asian Journal of Control

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This paper analyzes the asymptotic mean-square stabilizability and mixed performance of switched time-delay systems with time-varying random delay via a switching signal selection. Some delay-dependent LMI-based criteria are proposed to achieve the switching signal design. Our approach is proposed to guarantee the mixed performance of the system under consideration by Wirtinger-based inequality. A numerical example is given to show the main contribution of this paper.

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“…As is well known, chaos synchronization is a hot topic in recent years and receives much attention for the reason of its wide applicability in many scientific areas such as neural network [1]- [5], biomedical [6] and spacecraft [7]. Chaos demonstrates the oscillatory behavior which is unavoidable in dynamic nonlinear systems and shows a great sensitivity to initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Synchronization Control Design Based On Observers For Time-delay Lur’e Systems

et al. 2020

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This paper researches synchronization control design for chaotic Lur'e systems (CLSs) with time-varying delay. Considering of the unmeasurable state variables, Luenberger-type observers are designed for the master-slave systems. The synchronization has been achieved by using the proposed controller with the estimated system states. Based on Bessel-Legendre inequality, improved reciprocally convex combination approach and a novel double integral inequality, new Lyapunov Krasovskii functionals(LKFs) are tailored and a synchronization control criterion with less conservatism is obtained. Some simulations are given to verify that this control strategy we proposed is effective. INDEX TERMS Luenberger observer, chaotic synchronization, improved reciprocally convex approach, double integral inequality.

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Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Cited by 13 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

Mixed performance analysis of continuous switched systems with time‐varying random delay

Synchronization Control Design Based On Observers For Time-delay Lur’e Systems

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