Finite-time stability and boundedness for linear switched singular positive time-delay systems with finite-time unstable subsystems

Yimnet, Suriyon; Niamsup, Piyapong

doi:10.1080/21642583.2020.1839812

Cited by 10 publications

(12 citation statements)

References 52 publications

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“…The result can provide deep insight into the process of suppression of secondary tumours by the primary tumour. Time delay always accompanies with anti-angiogenic system in tumour growth, which may lead to oscillation and instability Qian, Li, Zhao, et al, 2020;Suriyon & Piyapong, 2020). But these may require different method, it needs to be discussed in the future work.…”

Section: Resultsmentioning

confidence: 99%

Asymptotic dynamics of an anti-angiogenic system in tumour growth

Zhang

2021

Systems Science & Control Engineering

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This paper deals with the Neumann initial boundary problem for anti-angiogenic system in tumour growth. The known results show that the problem possesses a unique global-in-time bounded classical solution for some sufficiently smooth initial data. For the large time behaviour of the global solution, by establishing some estimates based on semigroup theory, we prove that the solution approaches to the homogeneous steady state (n 0 , 0, 0) as t → ∞, wheren 0 is the spatial mean of the initial data for the endothelial cell tip density.

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Section: Resultsmentioning

confidence: 99%

Asymptotic dynamics of an anti-angiogenic system in tumour growth

Zhang

2021

Systems Science & Control Engineering

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“…The subsystems of the studied system are both finite-time bounded and finite-time unbounded. First, a class of quasi-alternative switching signals (QASSs) for system (1) is designed by utilizing a similar approach studied in [33,41].…”

Section: Resultsmentioning

confidence: 99%

“…As in [33,41], in our switching scheme, we design slow and fast switching for bounded subsystems and unbounded subsystems, respectively. It gives the lower bounds that bounded subsystems should dwell on and provides the upper bounds for unbounded subsystems.…”

Section: Remarkmentioning

confidence: 99%

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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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“…Close problems often appear concerning the properties of the controllability and reachability of dynamic systems. See, for instance, [24][25][26][27][28] and some of the references therein as well as the recent works [29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples

Sen

Ibeas

2022

Mathematics

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In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed.

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Finite-time stability and boundedness for linear switched singular positive time-delay systems with finite-time unstable subsystems

Cited by 10 publications

References 52 publications

Asymptotic dynamics of an anti-angiogenic system in tumour growth

Asymptotic dynamics of an anti-angiogenic system in tumour growth

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

On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples

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