Finite-time stability of switched nonlinear systems with finite-time unstable subsystems

Li, Xueling; Lin, Xiangze; Li, Shihua; Zou, Yun

doi:10.1016/j.jfranklin.2014.12.011

Cited by 52 publications

(17 citation statements)

References 43 publications

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“…Theorem 1 in the work of Lee et al 45 can be obtained directly from Corollary 2, when the function Γ(t) in the condition (ii) is a constant function, that is, Γ(t) = c 3 , c 3 is a constant. Moreover, Corollary 2 is less conservative than the results in the work of Li et al 46 For example, consider the FTS property for the SNS as follows:…”

Section: Corollary 2 For the Given Positive Scalars Nmentioning

confidence: 98%

“…which is Example 1 in the work of Li et al 46 and we choose c 1 = 1, c 2 = 50, T = 1. We calculate the total dwell time of the finite-time unstable subsystems using the results in the work of Li et al 46 and Corollary 2. By results in the work of Li et al, 46 we have T + [0, t) ≤ 0.1824.…”

Section: Corollary 2 For the Given Positive Scalars Nmentioning

confidence: 99%

“…We calculate the total dwell time of the finite-time unstable subsystems using the results in the work of Li et al 46 and Corollary 2. By results in the work of Li et al, 46 we have T + [0, t) ≤ 0.1824. At the same time, if we utilize Corollary 2, we obtain T + [0, t) ≤ 0.2036.…”

Section: Corollary 2 For the Given Positive Scalars Nmentioning

confidence: 99%

See 2 more Smart Citations

Finite‐time stability of switched nonlinear time‐delay systems

Wang

Sun

Chen

et al. 2020

Intl J Robust & Nonlinear

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This article addresses the problem of finite-time stability (FTS) and finite-time contractive stability (FTCS) for switched nonlinear time-delay systems (SNTDSs). By virtues of the Lyapunov-Razumikhin method, Lyapunov functionals approach, and the comparison principle technique, we obtain some improved Razumikhin-type theorems that verify FTS and FTCS property for SNTDSs. Moreover, our results allow the estimate of the upper bound of the derivatives for Lyapunov functions to be mode dependent functions which can be positive and negative. Meanwhile, the proposed results also improve the related existing results on the same topic by removing some restrictive conditions. Finally, two examples are presented to verify the effectiveness of our methods. K E Y W O R D S finite-time stability, Razumikhin technique, switched nonlinear systems, time-delay systems 1 2906

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Section: Corollary 2 For the Given Positive Scalars Nmentioning

confidence: 98%

Section: Corollary 2 For the Given Positive Scalars Nmentioning

confidence: 99%

See 1 more Smart Citation

Finite‐time stability of switched nonlinear time‐delay systems

Wang

Sun

Chen

et al. 2020

Intl J Robust & Nonlinear

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“…Recently, many kinds of finite-time issues have attracted particular research interests, and there have been some results on finite-time stabilization and synchronization [40][41][42][43][44][45][46][47]. However, to the best of the authors knowledge, there have been very few results on the finite-time stability problem for delayed GRNs with time delays [48,49], and the purpose of this study is therefore to shorten such a gap.…”

Section: Introductionmentioning

confidence: 99%

Finite‐Time Stability Analysis of Switched Genetic Regulatory Networks with Time‐Varying Delays via Wirtinger’s Integral Inequality

et al. 2021

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The problem of finite-time stability of switched genetic regulatory networks (GRNs) with time-varying delays via Wirtinger’s integral inequality is addressed in this study. A novel Lyapunov–Krasovskii functional is proposed to capture the dynamical characteristic of GRNs. Using Wirtinger’s integral inequality, reciprocally convex combination technique and the average dwell time method conditions in the form of linear matrix inequalities (LMIs) are established for finite-time stability of switched GRNs. The applicability of the developed finite-time stability conditions is validated by numerical results.

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“…Due to its good robustness nature, some impressive results about FT stability have been presented in many papers recently. 22–29 Given the singular analysis technique and Lyapunov theory, some sufficient conditions about robust finite-time stability of singular nonlinear systems have been studied in the work by Yang et al 29 Li et al 30 considered the problems on finite-time stability and boundedness for switched nonlinear systems with unstable subsystems by virtue of Lyapunov-like functions, respectively. Using the singular value decomposition approach, the sufficient conditions for the finite-time stability of the singular nonlinear switched time-delay systems were discussed in the work by Thanh et al 28 Input–output finite-time stabilization for a class of nonlinear impulsive hybrid systems was developed in the work by Yao and Li 31 The concepts of FT stability and FT stabilization were extended to the distributed parameter systems, 20,32 and the state feedback controller was designed to guarantee the FT stabilization of the closed-loop distributed parameter systems in the sense of L 2 norm.…”

Section: Introductionmentioning

confidence: 99%

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

Zhou

Wang

Tian

2020

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

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Finite-time stability of switched nonlinear systems with finite-time unstable subsystems

Cited by 52 publications

References 43 publications

Finite‐time stability of switched nonlinear time‐delay systems

Finite‐time stability of switched nonlinear time‐delay systems

Finite‐Time Stability Analysis of Switched Genetic Regulatory Networks with Time‐Varying Delays via Wirtinger’s Integral Inequality

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

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