Impulsive effects on the stability and stabilization of positive systems with delays

Hu, Meng‐Jie; Xiao, Jiang‐Wen; Xiao, Renbin; Chen, Wu‐Hua

doi:10.1016/j.jfranklin.2017.03.019

Cited by 51 publications

(38 citation statements)

References 34 publications

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“…Impulsive systems often arise in population dynamics, economics, electrical, etc. Therefore, impulsive systems also attract a lot of attention in the past few decades; we refer the reader to related works . Among them, continuous‐time impulsive positive systems have received some attentions .…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, impulsive systems also attract a lot of attention in the past few decades; we refer the reader to related works . Among them, continuous‐time impulsive positive systems have received some attentions . This is partly due to the fact that impulsive positive systems can be used to represent certain classes of population models, epidemiology, ecosystems, etc, which having deterministic jumps in their dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Zhang et al first investigated stability of impulsive positive linear systems; Briat further considered the dwell‐time stability of impulsive positive linear systems. Due to the importance of time delays in physics analysis, Wang et al, Hu et al, and Yang and Zhang further studied the stability of impulsive positive delay systems. It should be noted that those results in the works of Zhang et al, Briat, Hu et al, and Yang and Zhang are all based on the use of linear copositive Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the importance of time delays in physics analysis, Wang et al, Hu et al, and Yang and Zhang further studied the stability of impulsive positive delay systems. It should be noted that those results in the works of Zhang et al, Briat, Hu et al, and Yang and Zhang are all based on the use of linear copositive Lyapunov functions. However, for homogeneous positive delay systems, many technical results cannot be obtained by the linear copositive Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%

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Impulsive control of continuous‐time homogeneous positive delay systems of degree one

Yang

Zhang

2019

Intl J Robust & Nonlinear

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Summary This paper investigates the impulsive control of continuous‐time homogeneous positive delay systems of degree one. By using max‐separable Lyapunov functions and Razumikhin technique, a number of stability criteria for continuous‐time homogeneous impulsive positive delay systems of degree one are obtained. It should be noted that it is the first time that impulsive stabilization results for the addressed systems are given. Three numerical examples are presented to demonstrate the effectiveness of the control strategy.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Impulsive control of continuous‐time homogeneous positive delay systems of degree one

Yang

Zhang

2019

Intl J Robust & Nonlinear

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“…Although, the average impulsive interval approach has been applied to many existing literatures, there are no results concerning the time-varying impulses, where both stabilizing and destabilizing impulses are considered simultaneously. In addition, in most existing results on impulsive systems with average impulsive approach [4,15,16,35], it is assumed that the average impulsive interval is independent of the impulsive strength (we call it as strength-independent average impulsive interval), and the average impulsive intervals for all impulsive sequences are assumed to be equal to each other, which may not be anticipated. Actually, when considering time-varying impulsive effects, there are many impulses with different impulsive strengths.…”

Section: Introductionmentioning

confidence: 99%

Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals

Zhang¹,

Zhang²,

Li³

2018

J. Nonlinear Sci. Appl.

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This paper mainly deals with the stability of delayed neural networks with time-varying impulses, in which both stabilizing and destabilizing impulses are considered. By means of the comparison principle, the average impulsive interval and the Lyapunov function approach, sufficient conditions are obtained to ensure that the considered impulsive delayed neural network is exponentially stable. Different from existing results on stability of impulsive systems with average impulsive approach, it is assumed that impulsive strengths of stabilizing and destabilizing impulses take values from two finite states, and a new definition of impulsive strength-dependent average impulsive interval is proposed to characterize the impulsive sequence. The characteristics of the proposed impulsive strength-dependent average impulsive interval is that each impulsive strength has its own average impulsive interval and therefore the proposed impulsive strength-dependent average impulsive interval is more applicable than the average impulsive interval. Simulation examples are given to show the validity and potential advantages of the developed results.

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Finite‐time control via hybrid state feedback for uncertain positive systems with impulses

Park

2020

Intl J Robust & Nonlinear

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In this study, the finite‐time ℒ1 control for uncertain positive systems with impulses using a hybrid state feedback control mechanism is investigated. The hybrid state feedback double control strategy is utilized, which includes impulsive state control scheme and continuous state feedback control scheme. A type of time‐varying Lyapunov copositive function is constructed. Considering different impulsive effects, the finite‐time boundedness criterion is obtained by applying the average impulsive interval approach. In addition, sufficient conditions are proposed for finite‐time ℒ1 characterization analysis and the hybrid state feedback controller design. All the criteria can be checked by the linear programming approach succinctly. The relationships among the upper bound of the finite‐time interval, the frequency and intensity of impulses, and the minimum allowable ℒ1‐gain level are revealed. Numerical examples are used to illustrate the usefulness of the theoretical results.

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Impulsive effects on the stability and stabilization of positive systems with delays

Cited by 51 publications

References 34 publications

Impulsive control of continuous‐time homogeneous positive delay systems of degree one

Impulsive control of continuous‐time homogeneous positive delay systems of degree one

Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals

Finite‐time control via hybrid state feedback for uncertain positive systems with impulses

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