Mean square stabilization of linear systems by mean zero noise

Bobryk, Roman V.; Stettner, Łukasz

doi:10.1080/17442509908834209

Cited by 14 publications

(4 citation statements)

References 15 publications

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“…It is known [1,2,3,6,7], that for the moments of the solution to (1) we have an infinite chain of equations. To close this chain, we consider the so called closure problem.…”

Section: Consider the Following Linear Ordinary Equation In R D Dx (1mentioning

confidence: 99%

A Closure Method for Randomly Perturbed Linear Systems

Bobryk¹,

Stettener²

2001

Demonstratio Mathematica

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“…It is known [1,2,3,6,7], that for the moments of the solution to (1) we have an infinite chain of equations. To close this chain, we consider the so called closure problem.…”

Section: Consider the Following Linear Ordinary Equation In R D Dx (1mentioning

confidence: 99%

A Closure Method for Randomly Perturbed Linear Systems

Bobryk¹,

Stettener²

2001

Demonstratio Mathematica

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“…. If the excitation (2) is Ornstein-Uhlenbeck process, a similar hierarchy was obtained earlier in [2].…”

Section: Hierarchy For the Meanmentioning

confidence: 58%

Closure method and asymptotic expansions for linear stochastic systems

Bobryk

2007

Journal of Mathematical Analysis and Applications

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A closure procedure for the hierarchy of moment equations related to linear systems of ordinary differential equations with a random parametric excitation is introduced. A generalization of Pringsheim's theorem for continued fractions is used in a proof of the procedure convergence. The boundary function method for singular perturbation problems is applied to obtain asymptotic expansions for the moments of the solutions of such systems.

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“…Applying this formula to the Eq. (5) we obtain the following infinite chain of equations (see [27,28] for details):…”

Section: Mean Value Calculationsmentioning

confidence: 99%