Robust stability criteria for uncertain systems with interval time-varying delay based on multi-integral functional approach

Qian, Wei; Yuan, Manman; Wang, Lei; Chen, Yonggang; Yang, Junqi

doi:10.1016/j.jfranklin.2017.11.008

Cited by 20 publications

(9 citation statements)

References 32 publications

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“…A newly augmented LKF containing single, double and triple forms is constructed, and combined the improved Wirtinger inequality and extended reciprocally convex. Since the information of lower bound of time delay is considered in LKF, Theorem 1 can deal with the case that the lower bound of time delay is not restricted to be 0, but some recent results cannot deal with this case (An et al, 2014;Qian et al, 2018). It will be shown Theorem 1 can provide less conservatism results through some numerical examples.…”

Section: Resultsmentioning

confidence: 98%

Further results on delay-dependent robust H_∞ control for uncertain systems with interval time-varying delays

Qian

Xing

et al. 2020

Systems Science & Control Engineering

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This work focuses on the delay-dependent robust H ∞ control for uncertain linear systems with interval time-varying delays. The key features of the method include employment of a tighter integral inequality and construction of an appropriate Lyapunov-Krasovskii functionals (LKF). Meanwhile, the delay-dependent conditions with less conservatism are derived owing to the consideration of the information of the lower bound of time delay. Based on the obtained criteria, robust H ∞ controller design and performance analysis for the uncertain system are presented. Some numerical examples are also provided to show the effectiveness and advantage of the main results.

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Section: Resultsmentioning

confidence: 98%

Further results on delay-dependent robust H_∞ control for uncertain systems with interval time-varying delays

Qian

Xing

et al. 2020

Systems Science & Control Engineering

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“…Remark 4. In order to obtain further relaxed stability results based on Lyapunov-Krasovskii functionals method, an augmented Lyapunov-Krasovskii functional was constructed in [35], which contains single, double, triple and quadruple-integral terms. Meanwhile, multiple integral inequalities were introduced to estimate the integral terms of the derivative of Lyapunov-Krasovskii functional.…”

Section: Membership-function-dependent Stability Analysismentioning

confidence: 99%

New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

Zhou

Wang

2021

IET Control Theory & Appl

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This paper investigates the stability analysis and stabilization of T-S fuzzy systems with time-varying delays. First, a new augmented Lyapunov-Krasovskii functional is constructed, delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) are obtained by combining them with the integral inequality technique and the reciprocally convex combination inequality. Based on the state space decomposition method, some piecewise membership functions are employed to approximate the membership functions. The piecewise membership functions can be locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions. The boundary information of the membership functions is adequately taken into consideration in stability analysis, and then some relaxed membership-function-dependent stability results are obtained. Second, state feedback controllers for fuzzy systems with time-varying delays are presented under the imperfect premise-matching technique, whose membership functions and the number of fuzzy rules are allowed to be designed freely, consequently, the flexibility of controller design is improved. Finally, four numerical examples are given to demonstrate the effectiveness of the presented approaches.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…In this context, one of the difficulties lies in an accurate mathematical manipulation of the bounds of the integral terms that appear in the LKF derivatives. For instance, among the most popular techniques, we can found from the literature many approaches that considers Jensen's inequalities and/or their extensions, [9][10][11] Wirtinger inequalities, 3,[12][13][14] free-matrix-based integral inequalities, 5,15 reciprocally convex combinations 6,[16][17][18] and, more recently, Bessel-Legendre inequalities. 19 Furthermore, the stability conditions can be also relaxed by applying some useful techniques such like Finsler's lemma.…”

Section: Introductionmentioning

confidence: 99%

Improved robustH_∞stability analysis and stabilization of uncertain systems with stochastic input time‐varying delays

Bourahala

Rouamel

Guelton

2021

Optim Control Appl Methods

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This article focus on the robust H ∞ stability analysis and controller design for a class of uncertain and disturbed continuous-time systems with input time-varying delays characterized by stochastic Bernoulli distributions. First, robust H ∞ stability conditions for linear continuous systems with interval input time-varying delays is investigated. A delay-distribution-approach is considered to reduce the conservatism of the stability conditions from the convenient selection of a Lyapunov-Krasovskii functional (LKF), which considers both the lower and upper bounds of the stochastic time-varying delay to derive new delay-dependent H ∞ stability conditions in terms of linear matrix inequalities (LMIs). Then, derived from the proposed stability conditions, LMI-based conditions for the design of stabilizing robust H ∞ delayed state feedback controller are proposed. Finally, five numerical examples are considered to show the effectiveness of the proposed stability analysis and controller design conditions, in comparison to previous related results.

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Robust stability criteria for uncertain systems with interval time-varying delay based on multi-integral functional approach

Cited by 20 publications

References 32 publications

Further results on delay-dependent robust H_∞ control for uncertain systems with interval time-varying delays

Further results on delay-dependent robust H_∞ control for uncertain systems with interval time-varying delays

New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

Improved robustH_∞stability analysis and stabilization of uncertain systems with stochastic input time‐varying delays

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Robust stability criteria for uncertain systems with interval time-varying delay based on multi-integral functional approach

Cited by 20 publications

References 32 publications

Further results on delay-dependent robust H∞ control for uncertain systems with interval time-varying delays

Further results on delay-dependent robust H∞ control for uncertain systems with interval time-varying delays

New relaxed stability and stabilization conditions for T‐S fuzzy systems with time‐varying delays

Improved robustH∞stability analysis and stabilization of uncertain systems with stochastic input time‐varying delays

Contact Info

Product

Resources

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Further results on delay-dependent robust H_∞ control for uncertain systems with interval time-varying delays

Further results on delay-dependent robust H_∞ control for uncertain systems with interval time-varying delays

Improved robustH_∞stability analysis and stabilization of uncertain systems with stochastic input time‐varying delays