Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality

Sun, Yonghui; Li, Ning; Shen, Mouquan; Wei, Zhinong; Sun, Guoqiang

doi:10.1016/j.amc.2018.04.027

Cited by 33 publications

(47 citation statements)

References 49 publications

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“…Premultiplying and postmultiplying (32) and  ∈ ℝ n×n ,K = K, where  =  −1 , and we get the inequality (8). Therefore, we can get that the NCS (7) without uncertainties (ie, ΔA 1 (t) = ΔB 1 (t = ΔC 1 (t) = 0) is asymptotically stable with the control input (2).…”

Section: Robust Reliable H ∞ Control Methods For Known Actuator Faultsmentioning

confidence: 96%

“…Furthermore, if we set g(u(t))) = 0, then it will turned as a usual reliable control method. 7,8,18 Therefore, the proposed controller design (2) is a generalization of existing results in the literature.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 95%

“…Specifically, the linear part denotes the missing control gain actuators, and the nonlinear part denotes that the nonlinear deviations due to some technical problems. Furthermore, if we set g ( u ( t )))=0, then it will turned as a usual reliable control method . Therefore, the proposed controller design is a generalization of existing results in the literature.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 95%

“…For given constant 1 > 0 and 1 , the system (38) is asymptotically stable, if there exist positive symmetric 1, 3), any matrices kl , kl , kl , (k, l = 1, 2),  1 , and  ∈ ℝ n×n such that the following LMIs hold: 8 ], and the remaining terms are the same in Corollary 1. Remark 6.…”

Section: Corollarymentioning

confidence: 99%

“…4,5 This form of control systems is often called networked control systems (NCSs), and its communication channels are interconnected sensors with controllers and/or controllers with actuators. However, placing of communication channels in limited bandwidth capacity is established with unavoidable negative or imperfection reaction for NCSs such as communication data missing, 6,7 uncertainties, 8,9 and network-induced delay. 10,11 This will lead to poor performance of the system and may affect the stability of nature.…”

Section: Introductionmentioning

confidence: 99%

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Robust reliable H_∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Arunagirinathan

Muthukumar

Joo

2019

Intl J Robust & Nonlinear

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Summary In this paper, the robust reliable H∞ controller is designed for the problem of nonlinear actuator fault case in the uncertain networked control systems with randomly occurring missing data. More precisely, the occurrence of missing measurements is modeled by a stochastic variable in terms of Bernoulli random distribution. Also, the consideration of a nonlinear term in the input control scheme is a novel work for the proposed model. Suitable robust reliable design of control for a practical actuator fault model is constructed to guarantee the asymptotic stability of the system with H∞ performance level. A new form of Lyapunov‐Krasovskii functional with triple integral terms are formulated, and the reciprocally convex technique is utilized to establish the sufficient stability criterion in the form of linear matrix inequalities. Finally, the effectiveness of the proposed control method is shown through numerical examples, and we can confirm that the derived condition attained less conservatism than the existing results.

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Section: Robust Reliable H ∞ Control Methods For Known Actuator Faultsmentioning

confidence: 96%

Section: Problem Formulation and Preliminariesmentioning

confidence: 95%

Section: Problem Formulation and Preliminariesmentioning

confidence: 95%

Section: Corollarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust reliable H_∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Arunagirinathan

Muthukumar

Joo

2019

Intl J Robust & Nonlinear

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Robust stability and H∞$$ {H}_{\infty } $$ performance evaluation for time‐varying‐delayed uncertain linear systems based on variable‐augmented‐based free‐weighting matrices

Chen,

Shangguan,

2024

Asian Journal of Control

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The problem of the robust stability and performance evaluation of time‐varying‐delayed uncertain linear systems (TVDULSs) is studied in this article. At first, to obtain a modified robust delay‐dependent condition of TVDULSs, a novel augmented Lyapunov‐Krasovskii functional (LKF) is established, and a variable‐augmented‐based free‐weighting matrices (VAFWMs) technique is tailored to evaluate the functional derivative. Compared with the existing robust stability methods, the constructed functional takes fully time delay information of the system into consideration and provides more delay‐cross terms, where the corresponding matrices are used to relax the constraints of linear matrix inequalities in the stability condition. Also, the VAFWMs method fully considers the linear relation of some delayed integral terms in the functional derivative, which avoids the usage of a quadratic order or higher order terms of the time delay. Then, an improved performance analysis criterion of TVDULSs is obtained against the disturbance on the basis of the proposed robust stability condition. The admissible maximal delay upper bounds that the uncertain linear system can tolerate are provided by proposed criterion under a given performance level. At last, two numerical examples are presented to verify the effectiveness and the superiority of the methods obtained.

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Robust reliableH_∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay

Sun

Zhang

et al. 2021

Optim Control Appl Methods

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In this article, the problems of robust reliable H∞ optimization control for discrete‐time nonlinear systems with or without time‐delay subject to faults are investigated. A static state feedback controller is explored for Takagi–Sugeno fuzzy systems against nonlinear dynamics, exogenous disturbances, and model uncertainties. In contrast to the design of conventional controllers, the proposed controller is easier and more flexible. The Lyapunov function is utilized to assure the stability of the closed‐loop systems. Besides, linear matrix inequalities are utilized to derive the sufficient conditions by MATLAB toolbox. Finally, two simulation examples are shown to validate the feasibility of the suggested approach.

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Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality

Cited by 33 publications

References 49 publications

Robust reliable H_∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Robust reliable H_∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Robust stability and H∞$$ {H}_{\infty } $$ performance evaluation for time‐varying‐delayed uncertain linear systems based on variable‐augmented‐based free‐weighting matrices

Robust reliableH_∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay

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Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality

Cited by 33 publications

References 49 publications

Robust reliable H∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Robust reliable H∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Robust stability and H∞$$ {H}_{\infty } $$ performance evaluation for time‐varying‐delayed uncertain linear systems based on variable‐augmented‐based free‐weighting matrices

Robust reliableH∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay

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Robust reliable H_∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Robust reliable H_∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

Robust reliableH_∞optimization control for uncertain discrete‐time Takagi–Sugeno fuzzy systems with time‐varying delay