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

Yang, Gengjiao; Hao, Fei; Zhang, Linlin; Li, Bohu

doi:10.1109/access.2019.2953090

Cited by 8 publications

(3 citation statements)

References 32 publications

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“…In practical engineering, situations are often encountered where SPLSs with unstable subsystems must be dealt with due to factors such as disturbances, unmodelled dynamics and potential faults, the most common multi-phase traffic system controlled by traffic signals is a SPLS where all subsystems are unstable. Meanwhile, systems containing unstable subsystems have been shown to lead to reduced reliability and even failure of the entire system [15,16]. Due to the existence of unstable subsystems, the stable switching rate of a general SPLS is no longer equally applicable to a SPLS containing unstable subsystems, and the same FTS condition for a general SPLS is no longer applicable to a SPLS containing unstable subsystems, and the research results on SPLS containing unstable subsystems are not sufficiently rich at present.…”

Section: Introductionmentioning

confidence: 99%

Finite Time Stability Analysis Based on Dwell-Time Dependent Co-Positive Lyapunov Function

Zhang,

Liu

2024

Advances in Transdisciplinary Engineering

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Traffic signal control has always been the core problem of urban traffic control, in order to propose a more efficient signal intersection control method, this paper abstracts the signal intersection queue vehicle dissipation and waiting problem into a class of finite-time stability (FTS) problems for switching positive systems containing unstable subsystems. A new dwell-time dependent co-positive Lyapunov function (DTDCLF) is introduced, which can effectively solve the analysis of dwell-time dependent problems and can more effectively use the switching rule to construct the Lyapunov function. Sufficient conditions for the FTS of switched positive systems containing unstable subsystems in discrete-time and continuous-time contexts are obtained by this method, respectively. Lastly, an illustrative numerical example is presented to showcase the efficiency of the method. The method outlined in this paper provides a more efficient solution to the signal timing problem at oversaturated intersections, allowing vehicles at oversaturated intersections to be evacuated more quickly, reducing traffic delays and improving intersection efficiency.

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Section: Introductionmentioning

confidence: 99%

Finite Time Stability Analysis Based on Dwell-Time Dependent Co-Positive Lyapunov Function

Zhang,

Liu

2024

Advances in Transdisciplinary Engineering

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“…In [29], Liu et al employed the multiple discretized co-positive Lyapunov-Krasovskii functional (MDCPLKF) and dwell time (DT) switching to derive the delay-dependent sufficient criteria (DDSC) of the continuous-time and discrete-time SPTVDSs with AUMs. Later, a sufficient criterion ensuring the global uniform ES of the continuous-time SPTVDSs with AUMs by using the time-scheduled multiple co-positive Lyapunov-Krasovskii functional (TSMCPLKF) method and fast average dwell time (FADT) switching was obtained in [30]. However, among these studies, the IUs have been ignored.…”

Section: Introductionmentioning

confidence: 99%

A Switching Strategy for Stabilization of Discrete-Time Switched Positive Time-Varying Delay Systems with All Modes Being Unstable and Application to Uncertain Data

Mouktonglang

Poochinapan

Yimnet

2023

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The stability problem of switched systems plays an essential role in the study of long-term behavior. In fact, systems containing both time delay and uncertainty terms may lead to performance degradation of those systems. Therefore, we are interested in the robust stability for discrete-time switched positive time-varying delay systems with interval uncertainties in the case of all modes being unstable. Based on the proposed time-scheduled multiple co-positive Lyapunov–Krasovskii functional of each mode, new sufficient conditions for the global uniform asymptotic stability of the systems are derived. An effective time-dependent switching law utilized in this work is mode-dependent dwell time. In addition, the robust stability criteria in an asymptotic sense are formulated for the systems without time-varying delay. Compared with the existing related works, our results are less conservative and more general than some previous research. Finally, two numerical examples are provided to illustrate the effectiveness and correctness of the developed theoretical results.

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“…Nevertheless, the existence of the time delay in the systems may cause chaos and instability. Therefore, several beneficial results on SPSs, including time delay as well as time-varying delay, have been published, see [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Boundedness of Linear Uncertain Switched Positive Time-Varying Delay Systems with Finite-Time Unbounded Subsystems and Exogenous Disturbance

Mouktonglang

Yimnet

2021

Mathematics

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The problem of finite-time boundedness for a class of linear switched positive time-varying delay systems with interval uncertainties and exogenous disturbance is addressed. This characteristic research is that the studied systems include the finite-time bounded subsystems and finite-time unbounded subsystems. Both a slow mode-dependent average dwell time and a fast mode-dependent average dwell time switching techniques are utilized reasonably. And by applying a copositive Lyapunov-Krasovskii functional, novel delay-dependent sufficient criteria are derived to guarantee such systems to be finite-time bounded concerning the given parameters and designed switching signal. Furthermore, new finite-time boundedness criteria of the systems without interval uncertainties are also obtained. Finally, the efficiency of the theoretical results is presented in two illustrative examples.

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

Cited by 8 publications

References 32 publications

Finite Time Stability Analysis Based on Dwell-Time Dependent Co-Positive Lyapunov Function

Finite Time Stability Analysis Based on Dwell-Time Dependent Co-Positive Lyapunov Function

A Switching Strategy for Stabilization of Discrete-Time Switched Positive Time-Varying Delay Systems with All Modes Being Unstable and Application to Uncertain Data

Finite-Time Boundedness of Linear Uncertain Switched Positive Time-Varying Delay Systems with Finite-Time Unbounded Subsystems and Exogenous Disturbance

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