Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching
By Xuerong Mao, Yi Shen, Chenggui Yuan. 2008
169 citations recorded by the source corpus.
The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching. Linear NSDDEs with Markovian switching and nonlinear examples will be discussed to illustrate the theory.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/2c30a41f40bdcff9194faec1af5f5fc09f64abac
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In Applied Mathematics
In Computational Theory and Mathematics
In Control and Systems Engineering
Citations in the corpus
- Stability of neutral stochastic switched time delay systems: An average dwell time approach (2017, methodology): “Although some methods, such as Razumikhin-type theorem [3], Lyapunov-type theorem [4, 5, 10, 11], LMI approach [6–9], and integral inequality [12, 13] have been used to consider the exponential stability in moment for neutral stochastic delay differential systems, these proposed approaches are only ”
- Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters (2011, methodology): “Furthermore, the stability in distribution of solutions to stochastic neutral differential delay equations with Markovian switching parameters can be proved by Lyapunov function type methods [45].”
- Exponential H ∞ filtering for stochastic Markovian jump systems with time delays (2014, methodology): “On the basis of the martingale measure method used in [31], almost-sure exponential stability of neutral-type stochastic retarded Markovian jump systems is investigated in [29, 32].”
- Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations (2016, background): “Some of the stability criteria related to the pth moment exponential stability of the solutions to neutral stochastic functional differential equations (NSFDEs) were considered in [6–14] and the references therein.”
- Delay‐dependent stability of nonlinear hybrid neutral stochastic differential equations with multiple delays (2020, background): “Under Assumptions 1-2, the hybrid NSDE with multiple delays (2) with the initial data (3) has the properties: (1) it has the unique global solution {x(t)}t≥−τ .”