On the asymptotic stability of solutions of stochastic differential delay equations of second order

Tunç, Osman; Tunç, Cemil

doi:10.1080/16583655.2019.1652453

Cited by 28 publications

(11 citation statements)

References 34 publications

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“…In addition, we emphasize the effectiveness of the proposed algorithm by a numerical simulation. As a matter of fact, only some basic results have been achieved in the study of complex systems, such as the stability analysis of switched impulsive systems [29] and stochastic stability analysis of nonlinear second-order stochastic differential delay systems [30]. Therefore, it would be of interest to extend the proposed method to investigate more complex switched impulsive systems and nonlinear stochastic delay systems.…”

Section: Discussionmentioning

confidence: 99%

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A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

Zhao

et al. 2020

Adv Differ Equ

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We investigate non-Gaussian noise second-order filtering and fixed-order smoothing problems for non-Gaussian stochastic discrete systems with packet dropouts. We present a novel Kalman-like nonlinear non-Gaussian noise estimation approach based on the packet dropout probability distribution and polynomial filtering technique. By means of properties of Kronecker product we first introduce a second-order polynomial extended system and then analyze the means and variances of the Kronecker powers of the extended system noises. To generate noise estimators in forms of filtering and smoothing, we use the innovation approach. We give an example to illustrate that the presented algorithm has better robustness against packet dropouts than conventional linear minimum variance estimation.

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Section: Discussionmentioning

confidence: 99%

“…Taking into account that w(i), u e (i + j), and w e (i + j) are uncorrelated to each other, we can obtain (30) by substituting (33) into (28). Furthermore, fixed-lag smoother expression (29) follows directly by substituting (32) into (31).…”

Section: Theoremmentioning

confidence: 99%

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

Zhao

et al. 2020

Adv Differ Equ

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“…For more information on stability and boundedness to a kind of stochastic delay differential equations, see Ademola et al [6], Arnold [10], Mao [40,41] and Tunç and Tunç [48].…”

Section: Introductionmentioning

confidence: 99%

On the behaviour of solutions to a kind of third order neutral stochastic differential equation with delay

Mahmoud

Ademola

2022

Adv Cont Discr Mod

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This article demonstrates the behaviour of solutions to a kind of nonlinear third order neutral stochastic differential equations. Setting $x^{\prime }(t)=y(t)$ x ′ ( t ) = y ( t ) , $y^{\prime }(t) =z(t)$ y ′ ( t ) = z ( t ) the third order differential equation is ablated to a system of first order differential equations together with its equivalent quadratic function to derive a suitable downright Lyapunov functional. This functional is utilised to obtain criteria which guarantee stochastic stability of the trivial solution and stochastic boundedness of the nontrivial solutions of the discussed equations. Furthermore, special cases are provided to verify the effectiveness and reliability of our hypotheses. The results of this paper complement the existing decisions on system of nonlinear neutral stochastic differential equations with delay and extend many results on third order neutral and stochastic differential equations with and without delay in the literature.

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“…Liu and Caraballo [9] used the classical technique of Galerkin approximations to prove the existence of asymptotic stability of delay 2D Navier-Stokes system by exploiting 2 approaches. Asymptotic stability of second and third-order stochastic differential equations has been studied using a suitable Lyapunov-Krasovskii function to investigate the 0 solution [10,11]. Dami et al [12] derived the asymptotic stability and stabilization criteria based on the Lyapunov-Krasovskii function for a class of positive fractional order of 2D linear systems with and without delays.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Stability of 3D Stochastic Positive Linear Systems with Delays

Hameed

2022

Trends Sci

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The article emphasizes that 3D stochastic positive linear system with delays is asymptotically stable and depends on the sum of the system matrices and at the same time independent on the values and numbers of the delays. Moreover, the asymptotic stability test of this system with delays can be abridged to the check of its corresponding 2D stochastic positive linear systems without delays. Many theorems were applied to prove that asymptotic stability for 3D stochastic positive linear systems with delays are equivalent to 2D stochastic positive linear systems without delays. The efficiency of the given methods is illustrated on some numerical examples. HIGHLIGHTS Various theorems were applied to prove the asymptotic stability of 3D stochastic positive linear system with delays. Moreover, this system can be reduced to 2D stochastic positive linear system without delays Asymptotic stability of 3D stochastic positive linear systems with delays depends on the summation of system matrices and independent on numbers and values of delays for that system The principal minors and the coefficients for characteristic polynomials of 3D stochastic linear systems were applied to demonstrate the asymptotic stability when they are all positive

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On the asymptotic stability of solutions of stochastic differential delay equations of second order

Cited by 28 publications

References 34 publications

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

A study on input noise second-order filtering and smoothing of linear stochastic discrete systems with packet dropouts

On the behaviour of solutions to a kind of third order neutral stochastic differential equation with delay

Asymptotic Stability of 3D Stochastic Positive Linear Systems with Delays

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