Stabilization of systems with interval time-varying delay based on delay decomposing approach

Qian, Wei; Yuan, Manman; Wang, Lei; Bu, Xuhui; Yang, Junqi

doi:10.1016/j.isatra.2017.05.017

Cited by 41 publications

(28 citation statements)

References 24 publications

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“…"> 2.We reveal that the utilized k th‐order reciprocity convex method is very effective with the integral inequalities, which give the less conservatism than the other techniques . In particular, the obtained results are showing the superiority of delay‐dependent stability criteria than that by Raja et al with free‐weighting matrix method, that by Zhang et al with extended Wirtinger's integral inequalities, and that by Qian et al with decomposing the delay interval into multiple equidistant subinterval method. 3.Numerical examples and simulation results are carried out to prove the importance of proposed stability analysis through comparisons with existing results .…”

Section: Resultsmentioning

confidence: 72%

“…In particular, the obtained results are showing the superiority of delay‐dependent stability criteria than that by Raja et al with free‐weighting matrix method, that by Zhang et al with extended Wirtinger's integral inequalities, and that by Qian et al with decomposing the delay interval into multiple equidistant subinterval method. 3.Numerical examples and simulation results are carried out to prove the importance of proposed stability analysis through comparisons with existing results . It is also highlighted to find the MAUBs and the improved H ∞ performance index level. …”

Section: Resultsmentioning

confidence: 72%

“…The main idea of the deriving proof is how to handle the integral terms (see Appendix C). The single integral terms and double integral terms are rewritten as the sum of two terms and three terms (see Appendix C), and each of the terms is bounded using integral inequalities (see Lemmas and ) in LBL, which can help to obtain possible conservatism than the results …”

Section: Resultsmentioning

confidence: 99%

“…Remark The single‐integral terms

\int_{t - α_{1}}^{t} x false(s false) d s

and

\int_{t - α_{2}}^{t} x false(s false) d s

are introduced in Γ( t ) to obtain more cross terms among

\overset{x}{true} false(t false),

x ( t ), x ( t − α 1 ) and x ( t − α 2 ). Further, different from the work of Raja et al, Zhang et al, and Qian et al, many triple‐integral terms are introduced into the augmented LKF in Corollary and Corollary . Also, due to the appearance of these triple‐integral terms in LKF, the integral terms such as

\frac{1}{h_{1}} \int_{t - α_{1}}^{t - τ false(t false)} x^{T} false(s false) d s,

\frac{1}{τ false(t false)} \int_{t - τ false(t false)}^{t} x^{T} false(s false) d s,

\frac{1}{h_{2}} \int_{t - α_{2}}^{t - h false(t false)} x^{T} false(s false) d s,

\frac{1}{h false(t false)} \int_{t - h false(t false)}^{t} x^{T} false(s false) d s,

\frac{1}{h_{1}} \int_{- α_{1}}^{- τ false(t false)} \int_{t - α_{1}}^{t - τ false(t false)} x^{T} false(<...>

…”

Section: Resultsmentioning

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: Resultsmentioning

confidence: 72%

Section: Resultsmentioning

confidence: 72%

Section: Resultsmentioning

confidence: 99%

“…Remark The single‐integral terms

\int_{t - α_{1}}^{t} x false(s false) d s

and

\int_{t - α_{2}}^{t} x false(s false) d s

are introduced in Γ( t ) to obtain more cross terms among

\overset{x}{true} false(t false),

\frac{1}{h_{1}} \int_{t - α_{1}}^{t - τ false(t false)} x^{T} false(s false) d s,

\frac{1}{τ false(t false)} \int_{t - τ false(t false)}^{t} x^{T} false(s false) d s,

\frac{1}{h_{2}} \int_{t - α_{2}}^{t - h false(t false)} x^{T} false(s false) d s,

\frac{1}{h false(t false)} \int_{t - h false(t false)}^{t} x^{T} false(s false) d s,

\frac{1}{h_{1}} \int_{- α_{1}}^{- τ false(t false)} \int_{t - α_{1}}^{t - τ false(t false)} x^{T} false(<...>

…”

Section: Resultsmentioning

confidence: 99%

See 2 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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show abstract

“…Therefore, according to the Lyapunov stability theory [13][14][15], the closed-loop control system is stable from (28).…”

Section: Stabilitymentioning

confidence: 99%

Sliding‐Mode Control of the Active Suspension System with the Dynamics of a Hydraulic Actuator

Bai

Guo

2018

Complexity

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An improved model of the active suspension system is proposed. Compared with the existing model of active suspension system, the dynamics of a hydraulic actuator in the active suspension system is fully considered in the proposed model. Based on the proposed model, a sliding-mode control method is designed to control the active suspension system. Stability proof and analysis of the closed-loop system of the active suspension is given by using Lyapunov stability theory. At last, the reliability and feasibility of the proposed sliding-mode control method are evaluated by computer simulation. Simulation research shows that the proposed sliding-mode control method can obtain good control performance for the active suspension system.

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Improved robust stability criteria for uncertain linear neutral‐type systems via novel Lyapunov‐Krasovskii functional

Duan

Tang

Duan

2019

Asian Journal of Control

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The stability problem for the uncertain time‐varying delayed neutral‐type system is concerned in this paper. By introducing a novel Lyapunov‐Krasovskii functional (LKF) related to a delay‐product‐type function and two delay‐dependent matrices, some new delay‐dependent robust stability sufficient conditions are derived, which are based on convex linear matrix inequality (LMI) framework. The sufficient conditions in this paper can reduce the conservativeness of some recent previous ones. In the end, some numerical examples, including a linear neutral‐type system, the partial element equivalent circuit and a general linear system, show the effectiveness of the proposed method.

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Stabilization of systems with interval time-varying delay based on delay decomposing approach

Cited by 41 publications

References 24 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 of the Active Suspension System with the Dynamics of a Hydraulic Actuator

Improved robust stability criteria for uncertain linear neutral‐type systems via novel Lyapunov‐Krasovskii functional

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Stabilization of systems with interval time-varying delay based on delay decomposing approach

Cited by 41 publications

References 24 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 of the Active Suspension System with the Dynamics of a Hydraulic Actuator

Improved robust stability criteria for uncertain linear neutral‐type systems via novel Lyapunov‐Krasovskii functional

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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