Stability of the linear stochastic system

Kozin, F.

doi:10.1007/bfb0064943

Cited by 49 publications

(31 citation statements)

References 25 publications

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“…For further comments on the tradeoffs of studying the behavior of sample paths (almost -sure stability criteria) versus p t h mean stability, see Kozin [6,7 ] .…”

Section: -mentioning

confidence: 99%

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Stability Criteria for Continuous-Time Systems with Colored Multiplicative Noise.

Martin¹,

Johnson²

1977

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“…For further comments on the tradeoffs of studying the behavior of sample paths (almost -sure stability criteria) versus p t h mean stability, see Kozin [6,7 ] .…”

Section: -mentioning

confidence: 99%

“…In the literature [7], there have appeared plots of the mean square stability criteria for System (15) . superimposed on the criteria for the corresponding white noise parameter system (Ito sense) .…”

Section: Th Eorem_mentioning

confidence: 99%

Stability Criteria for Continuous-Time Systems with Colored Multiplicative Noise.

Martin¹,

Johnson²

1977

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“…The time-derivative of Liapunov functional has to be negative in some defined sense. Almost sure stability of the beam equilibrium state in the strong formulation was examined by Kozin [2]. The uniform stochastic stability analysis of laminated beams and plates described by partial differential equations with time and space dependent was presented in [3].…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability of weak equations of continuous systems

Tylikowski

2009

Arch Appl Mech

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The stability analysis method is developed for distributed dynamic problems with relaxed assumptions imposed on solutions. The problem is motivated by structural vibrations with external time-dependent parametric excitations which are controlled using surface-mounted or -embedded actuators and sensors. The strong form of equations involves irregularities which lead to computational difficulties for estimation and control problems. In order to avoid irregular terms resulting from differentiation of the force and moment terms the dynamics equations are written in a weak form. The weak form of dynamics equations of linear mechanical structures is obtained using variational calculus. The study of stability of stochastic weak system is based on examining properties of Liapunov functional along a weak solution.

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“…In the paper [5] by F. Kozin a few ideas and their application to the study of stability of linear stochastic systems were presented. In particular it was shown how they lead to stronger sufficient conditions, and in the case of the Ito differential equations, to the exact stability boundary for second order systems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Stability of Vector Sde With Applications to a Stochastic Epidemic Model

Swishchuk¹,

Svishchuk²,

Limnios³

2016

Int. J. of Pure and Appl. Math.

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In this paper we consider stochastic stability, namely, asymptotic stability in mean, asymptotic mean-square stability, asymptotic stability a.s., exponential p-stability and stability with stochastic Lyapunov fucntion for vector stochastic differential equations. We apply these results to the stochastic epidemic models induced by bacteriophages in the marine bacteria populations. The novelty of the paper consists of new stability results for vector SDE and their applications to a new stochastic epidemic model.

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Stability of the linear stochastic system

Cited by 49 publications

References 25 publications

Stability Criteria for Continuous-Time Systems with Colored Multiplicative Noise.

Stability Criteria for Continuous-Time Systems with Colored Multiplicative Noise.

Dynamic stability of weak equations of continuous systems

Stochastic Stability of Vector Sde With Applications to a Stochastic Epidemic Model

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