Nonfragile Sampled-Data Control for Uncertain Networked Control Systems With Additive Time-Varying Delays

Muthukumar, P.; Arunagirinathan, S.; Lakshmanan, S.

doi:10.1109/tcyb.2018.2807587

Cited by 31 publications

(14 citation statements)

References 38 publications

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“…Further, using , the LMI has been reformulated as

\overset{Ψ}{true} = Ψ + $_{1}^{* T} L $_{2} + $_{2}^{T} L^{T} $_{1}^{*} < 0

, where

$_{1}^{*} = false[0_{n \times 13 n} {false(C_{1} \overset{Φ}{true} false)}^{T} 0_{n \times 14 n} {false(γ C_{2} \overset{Φ}{true} false)}^{T} 0_{n \times n} false]

, and Ψ has been derived by using

\overset{Φ}{true}

instead of Φ in Ψ. Moreover, using lemma 4 in the work of Muthukumar et al, there exists a scalar ζ >0 such that

\begin{matrix} alignleft \\ align-1 \tilde{Ψ} = Ψ + ζ $_{1}^{* T} L $_{1}^{*} + ζ^{- 1} $_{2}^{T} L^{T} $_{2} < 0 . & align-2 \end{matrix}

Then, applying Schur complement lemma, it is easy to see that is equivalent to . This completes the proof.…”

Section: Resultsmentioning

confidence: 99%

“…Proof Replacing A 1 , B 1 and C 1 in with A 1 + FM ( t ) N a , B 1 + FM ( t ) N b , and C 1 + FM ( t ) N c , respectively, and using Theorem , we get the modified LMI conditions as

\overset{Ψ}{true} = \overset{Ψ}{true} + {\overset{$}{true}}_{1}^{T} M^{T} false(t false) {\overset{$}{true}}_{2}^{*} + {\overset{$}{true}}_{2}^{* T} M false(t false) {\overset{$}{true}}_{1} < 0

, where

{\overset{$}{true}}_{2}^{*} = false[0_{n \times 13 n} F^{T} 0_{n \times 18 n} false]

. Moreover, using Lemma 4 in the work of Muthukumar et al, that there exists a scalar ε >0 such that

\begin{matrix} alignleft \\ align-1 \tilde{Ψ} = Ψ + ε {\overset{ˇ}{$}}_{1}^{* T} L {\overset{ˇ}{$}}_{1}^{*} + ε^{- 1} {\overset{ˇ}{$}}_{2}^{T} L^{T} {\overset{ˇ}{$}}_{2} < 0 . & align-2 \end{matrix}

Then, applying Schur complement lemma, it is easy to see that is equivalent to . This completes the proof.…”

Section: Resultsmentioning

confidence: 99%

“…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, uncertainties, and network‐induced delay . This will lead to poor performance of the system and may affect the stability of nature.…”

Section: Introductionmentioning

confidence: 99%

“…Since NCSs are usually modeled by communication networks, network‐induced delays always exist and can affect system performance. So far, various achievements on induced delays have been obtained . Stability results for analyzing the qualitative nature of drift control systems are not sufficient to study the practical characteristics of a dynamic model.…”

Section: Introductionmentioning

confidence: 99%

“…The H ∞ control problems under missing measurements with Bernoulli distribution are studied for a linear systems subject to actuator saturation and for a nonlinear systems subject to sensor saturation. Inevitably, to derive the less conservatism of the control systems using various Lyapunov‐Krasovskii functionals (LKFs), different mathematical approaches have been utilized such as Jensen inequality, Wirtinger‐based inequality, delay‐dependent region partitioning approach, and reciprocal convexity method . Meanwhile, if the integral term containing a fractional form such as

\frac{1}{b - a} \int_{a}^{b} x false(θ false) d θ

and

\frac{1}{b - a} \int_{a}^{b} \int_{t + θ}^{t} x false(s false) d s d θ

in the augmented vector, the reciprocally convex method will be derived always, regardless of the degree of the inequality, and it is handled by the lower bound lemma (LBL) .…”

Section: Introductionmentioning

confidence: 99%

See 4 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

Self Cite

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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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“…Further, using , the LMI has been reformulated as

\overset{Ψ}{true} = Ψ + $_{1}^{* T} L $_{2} + $_{2}^{T} L^{T} $_{1}^{*} < 0

, where

$_{1}^{*} = false[0_{n \times 13 n} {false(C_{1} \overset{Φ}{true} false)}^{T} 0_{n \times 14 n} {false(γ C_{2} \overset{Φ}{true} false)}^{T} 0_{n \times n} false]

, and Ψ has been derived by using

\overset{Φ}{true}

instead of Φ in Ψ. Moreover, using lemma 4 in the work of Muthukumar et al, there exists a scalar ζ >0 such that

\begin{matrix} alignleft \\ align-1 \tilde{Ψ} = Ψ + ζ $_{1}^{* T} L $_{1}^{*} + ζ^{- 1} $_{2}^{T} L^{T} $_{2} < 0 . & align-2 \end{matrix}

Then, applying Schur complement lemma, it is easy to see that is equivalent to . This completes the proof.…”

Section: Resultsmentioning

confidence: 99%

“…Proof Replacing A 1 , B 1 and C 1 in with A 1 + FM ( t ) N a , B 1 + FM ( t ) N b , and C 1 + FM ( t ) N c , respectively, and using Theorem , we get the modified LMI conditions as

\overset{Ψ}{true} = \overset{Ψ}{true} + {\overset{$}{true}}_{1}^{T} M^{T} false(t false) {\overset{$}{true}}_{2}^{*} + {\overset{$}{true}}_{2}^{* T} M false(t false) {\overset{$}{true}}_{1} < 0

, where

{\overset{$}{true}}_{2}^{*} = false[0_{n \times 13 n} F^{T} 0_{n \times 18 n} false]

. Moreover, using Lemma 4 in the work of Muthukumar et al, that there exists a scalar ε >0 such that

\begin{matrix} alignleft \\ align-1 \tilde{Ψ} = Ψ + ε {\overset{ˇ}{$}}_{1}^{* T} L {\overset{ˇ}{$}}_{1}^{*} + ε^{- 1} {\overset{ˇ}{$}}_{2}^{T} L^{T} {\overset{ˇ}{$}}_{2} < 0 . & align-2 \end{matrix}

Then, applying Schur complement lemma, it is easy to see that is equivalent to . This completes the proof.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

\frac{1}{b - a} \int_{a}^{b} x false(θ false) d θ

and

\frac{1}{b - a} \int_{a}^{b} \int_{t + θ}^{t} x false(s false) d s d θ

in the augmented vector, the reciprocally convex method will be derived always, regardless of the degree of the inequality, and it is handled by the lower bound lemma (LBL) .…”

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

Self Cite

View full text Add to dashboard Cite

show abstract

Sliding Mode Control Under Denial-of-Service Attacks

Zong

2023

Studies in Systems, Decision and Control

View full text Add to dashboard Cite

Fixed-time synchronization in probability of drive-response networks with discontinuous nodes and noise disturbances

Feng

et al. 2019

Nonlinear Dyn

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Nonfragile Sampled-Data Control for Uncertain Networked Control Systems With Additive Time-Varying Delays

Cited by 31 publications

References 38 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

Sliding Mode Control Under Denial-of-Service Attacks

Fixed-time synchronization in probability of drive-response networks with discontinuous nodes and noise disturbances

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Nonfragile Sampled-Data Control for Uncertain Networked Control Systems With Additive Time-Varying Delays

Cited by 31 publications

References 38 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

Sliding Mode Control Under Denial-of-Service Attacks

Fixed-time synchronization in probability of drive-response networks with discontinuous nodes and noise disturbances

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Product

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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