An extended reciprocally convex matrix inequality and its application to stability analysis of systems with additive time-varying delays

Jiao, Jianmin; Zhang, Rui

doi:10.1016/j.jfranklin.2019.11.065

Cited by 13 publications

(12 citation statements)

References 30 publications

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“…Remark 1: Lemma 2.1 provides a new free-matrix-based integral inequality. Differently from the existing integral inequalities [37], [36] that only give estimates of the energy of the derivative of the state (i.e. b aẋ T (s)Rẋ(s)), this lemma successfully provides estimates of the energy of the vector that contains the state and its derivative at the same time…”

Section: A New Free-matrix-based Integral Inequalitymentioning

confidence: 98%

“…In [37], the entire interval of the ATD [−d 12 , 0] was divided into the following subintervals when constructing the LKF:…”

Section: Remarkmentioning

confidence: 99%

“…Remark 5: The LKF V (t) of Theorem 3.1 takes into account the double integral term with the vector ẋ T (s) x T (s) containing the state and its derivatives at the same time. This allows the LKF to consider more information of the system than the existing methods [36], [37] which considers the double integral with a vector that contains a single state i.e.…”

Section: Remarkmentioning

confidence: 99%

“…The paper [36] provided improved results over the existing works, but the results were obtained from application of some existing techniques. The authors of [37] introduced a new extended reciprocally convex matrix inequality. They constructed the LKF by partitioning the delay into the multiple subintervals and combined the introduced inequality with the Wirtinger-based integral inequality, which results in an improved stability criterion.…”

Section: Introductionmentioning

confidence: 99%

“…They constructed the LKF by partitioning the delay into the multiple subintervals and combined the introduced inequality with the Wirtinger-based integral inequality, which results in an improved stability criterion. On the other hands, in [38], the entire interval of the ATD divided into the four subintervals FIGURE 1: The schematic representation for systems with the additive time-varying delays sets including the subintervals set proposed in [37]. However, since some of the subintervals in [38] do not include the timedelayed state given in the system, these subintervals may be conservative.…”

Section: Introductionmentioning

confidence: 99%

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New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

2020

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This paper is concerned with the problem of stability analysis for systems with additive time-varying delays (ATDs). This paper proposes a new free-matrix-based integral inequality that provides estimate of the energy of the vector that contains the state and its derivative at the same time. Consequently, the proposed inequality enables the Lyapunov-Krasovskii functional (LKF) to take into account not only the respective energies of the state and its derivatives but also the correlated effect of them. Then, based on the proposed inequality, this paper derives a new stability criterion of systems with ATDs. This paper constructs LKF by proposing new sets of multiple subintervals of the ATDs, and makes use of the proposed inequality when estimating the derivatives of the LKF. This allows the resulting stability criterion to take full advantage of the information of the multiple subintervals of the ATDs. This paper also successfully applies the proposed free-matrix-based integral inequality to the system with a single time-varying delay. Three numerical examples demonstrate the effectiveness of the proposed methods.

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Section: A New Free-matrix-based Integral Inequalitymentioning

confidence: 98%

“…In [37], the entire interval of the ATD [−d 12 , 0] was divided into the following subintervals when constructing the LKF:…”

Section: Remarkmentioning

confidence: 99%