Stability Analysis of Switched Positive Nonlinear Systems by Mode-Dependent Average Dwell Time Method

Tian, Yazhou; Sun, Yuangong

doi:10.1109/access.2019.2894135

Cited by 21 publications

(9 citation statements)

References 28 publications

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“…Case 2: when t ∈ [t k + τ * , t k+1 ). Similar to Case 1, we can also derive (29) from (19). Finally, according to Definition 3, system (1) is GUES under the fast ADT satisfying (17).…”

Section: And Then Calculating the Derivative Of The Vector Functionmentioning

confidence: 85%

Exponential Stability for Continue-Time Switched Positive Delay Systems With All Unstable Subsystems

et al. 2019

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In this paper, the stability of continue-time switched positive delay systems (SPDSs) with all unstable subsystems is investigated. Based on the time-scheduled multiple co-positive Lyapunov-Krasovskii functional (MCLKF) method combined with fast average dwell time (ADT) techniques, a sufficient condition is obtained to ensure the underlying system is exponentially stable. Compared with the results in existing literature, our work has two advantages. On the one hand, the proposed method is independent of the maximum of corresponding elements of each subsystem matrix, which overcomes the limitation of the existing method. On the other hand, our result is less conservative than that of the previous literature. In addition, the stability condition of the system in this paper is given by matrix inequality, which can be solved by nonlinear programming. Finally, two simulation examples are provided to illustrate the correctness and effectiveness of the main result. INDEX TERMS Exponential stability, switched positive system, time-varying delay, unstable subsystems.

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“…Case 2: when t ∈ [t k + τ * , t k+1 ). Similar to Case 1, we can also derive (29) from (19). Finally, according to Definition 3, system (1) is GUES under the fast ADT satisfying (17).…”

Section: And Then Calculating the Derivative Of The Vector Functionmentioning

confidence: 85%

Exponential Stability for Continue-Time Switched Positive Delay Systems With All Unstable Subsystems

et al. 2019

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“…Two illustrated examples with some comparisons between the existing results and those proposed ones are presented to show the effectiveness and advantages of the obtained theoretical results. It is worth mentioning that this new technique can be applied to other systems, such as switched positive systems [31], switched uncertain systems [32], switched affine systems [33], Boolean networks [34]. In our future works, we will extend the proposed approach to discrete-time switched T-S fuzzy systems [30] and the stability of DTSSs with all unstable modes will be further investigated.…”

Section: Discussionmentioning

confidence: 99%

A Limit Φ-Dependent ADT Technique for Stability Analysis of Discrete-Time Switched Systems With Unstable Modes

Yan

2020

IEEE Access

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The stability problem of discrete-time switched systems with unstable modes is concerned under two novel switching strategies, i.e., limit inferior and superior Φ-dependent average dwell time switchings. Some improved stability criteria of discrete-time switched systems with unstable modes are obtained by combining a multiple Lyapunov function method with two strategies proposed, where limit inferior and superior switchings are applied to deal with stable and unstable modes, respectively. Especially, we also give stability conditions of discrete-time switched systems comprising stable modes. It is shown that these conditions with tighter bounds of average dwell time (ADT) and mode-dependent ADT cover some existing ones. Finally, two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results. INDEX TERMS Discrete-time switched systems, stability, multiple Lyapunov functions, Φ-dependent average dwell time.

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“…The application of the proposed approach in a numerical example with some comparisons among different illustrates its effectiveness and practicability. It is worth mentioning that this new approach can be extended to other situations based on ADT/MDADT ones, such as switched T-S fuzzy systems [25], [26], switched time-delay systems [27], [28], switched positive systems [29] and switched systems with unstable subsystems [8], [9], [24], etc.…”

Section: Discussionmentioning

confidence: 99%

Stability Analysis of Switched Systems Under Φ-Dependent Average Dwell Time Approach

Zhai

2020

IEEE Access

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The concept of the -dependent average dwell time ( DADT) is presented for both continuous-time and discrete-time switched systems. Some new stability criteria for switched systems are obtained under the DADT approach, which depends on the choice of the classification function . The relationships among the classic ADT approach, the mode-dependent ADT approach and the proposed one are also discussed, which shows that those existing approaches can be unified to the new one. More concretely, stability results based on ADT/MDADT schemes can be regarded as some special cases of our results with specific functions . The obtained switching design by the new approach is more flexible and practical. At last, a numerical example with some comparisons among the differences in the selection of is included to explain the validity and advantages of the new technique.INDEX TERMS Switched systems, stability, stable subsystems, -dependent average dwell time.

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Stability Analysis of Switched Positive Nonlinear Systems by Mode-Dependent Average Dwell Time Method

Cited by 21 publications

References 28 publications

Exponential Stability for Continue-Time Switched Positive Delay Systems With All Unstable Subsystems

Exponential Stability for Continue-Time Switched Positive Delay Systems With All Unstable Subsystems

A Limit Φ-Dependent ADT Technique for Stability Analysis of Discrete-Time Switched Systems With Unstable Modes

Stability Analysis of Switched Systems Under Φ-Dependent Average Dwell Time Approach

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