scholarly journals On Stability for Hybrid System under Stochastic Perturbations

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
Cao Tan Binh ◽  
Ta Cong Son
Keyword(s):  
Exponential Stability ◽  
Hybrid System ◽  
Communication Protocols ◽  
Stochastic Perturbations ◽  
Type Function ◽  
Almost Surely Exponential Stability ◽  
Transfer Interval ◽  
Nonlinear Hybrid

The aim of this paper is to find out suitable conditions for almost surely exponential stability of communication protocols, considered for nonlinear hybrid system under stochastic perturbations. By using the Lyapunov-type function, we proved that the almost surely exponential stability remain be guaranteed as long as a bound on the maximum allowable transfer interval (MATI) is satisfied.  

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

Exponential stability for nonlinear hybrid stochastic systems with time varying delays of neutral type

2020 ◽  
Vol 107 ◽  
pp. 106468
Author(s):  
Lichao Feng ◽  
Zhihui Wu ◽  
Jinde Cao ◽  
Shiqiu Zheng ◽  
Fuad E. Alsaadi
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Neutral Type ◽  
Time Varying ◽  
Hybrid Stochastic Systems ◽  
Nonlinear Hybrid

scholarly journals pth Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xuetao Yang ◽  
Quanxin Zhu ◽  
Zhangsong Yao
Keyword(s):  
Fixed Point ◽  
Exponential Stability ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Heat Equations ◽  
Stochastic Heat Equations ◽  
Pth Moment Exponential Stability ◽  
Infinite State ◽  
Moment Exponential Stability ◽  
Nonlinear Hybrid

We are concerned with the exponential stability problem of a class of nonlinear hybrid stochastic heat equations (known as stochastic heat equations with Markovian switching) in an infinite state space. The fixed point theory is utilized to discuss the existence, uniqueness, andpth moment exponential stability of the mild solution. Moreover, we also acquire the Lyapunov exponents by combining the fixed point theory and the Gronwall inequality. At last, two examples are provided to verify the effectiveness of our obtained results.

Asymptotic behavior, attracting and quasi-invariant sets for impulsive neutral SPFDE driven by Lévy noise

2017 ◽  
Vol 18 (01) ◽  
pp. 1850010 ◽  
Author(s):  
Diem Dang Huan ◽  
Ravi P. Agarwal
Keyword(s):  
Exponential Stability ◽  
Mild Solution ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Invariant Sets ◽  
Lévy Noise ◽  
Almost Surely Exponential Stability ◽  
Functional Differential ◽  
Levy Noise ◽  
Moment Exponential Stability

By establishing two new impulsive-integral inequalities, the attracting and quasi-invariant sets of the mild solution for impulsive neutral stochastic partial functional differential equations driven by Lévy noise are obtained, respectively. Moreover, we shall derive some sufficient conditions to ensure stability of this mild solution in the sense of both moment exponential stability and almost surely exponential stability.

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