Asymptotic stability in probability and stabilization for a class of discrete-time stochastic systems

2014 ◽  
Vol 25 (15) ◽  
pp. 2803-2815 ◽  
Author(s):  
J. Yin
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Stability In Probability ◽  
Asymptotic Stability In Probability

On the Partial Stochastic Stability of Stochastic Differential Delay Equations with Markovian Switching

2013 ◽  
Vol 765-767 ◽  
pp. 709-712 ◽  
Author(s):  
De Zhi Liu ◽  
Wei Qun Wang
Keyword(s):  
Asymptotic Stability ◽  
Stochastic Stability ◽  
Sufficient Conditions ◽  
Delay Equations ◽  
Markovian Switching ◽  
Differential Delay ◽  
Stability In Probability ◽  
Differential Delay Equations ◽  
Stochastic Differential Delay Equations ◽  
Asymptotic Stability In Probability

In the paper, we are concerned with the partial asymptotic stochastic stability (stability in probability) of stochastic differential delay equations with Markovian switching (SDDEwMSs), the sufficient conditions for partial asymptotic stability in probability have been given and we have generalized some results of Sharov and Ignatyev to cover a class of much more general SDDEwMSs.

Stochastic Response and Stability Analysis of Single Leg Articulated Tower

2003 ◽  
Author(s):  
A. K. Banik ◽  
T. K. Datta
Keyword(s):  
Asymptotic Stability ◽  
Probability Density ◽  
Parametric Excitation ◽  
Stochastic Averaging ◽  
Stochastic Response ◽  
Sea State ◽  
Stationary Response ◽  
Stability In Probability ◽  
Hydrodynamic Damping ◽  
Asymptotic Stability In Probability

The stationary response and asymptotic stability in probability of an articulated tower under random wave excitation are investigated. The articulated tower is modelled as a SDOF system having stiffness nonlinearity, damping nonlinearity and parametric excitation. Using a stochastic averaging procedure and Fokker-Plank-Kolomogorov equation (FPK), the probability density function of the stationary solution is obtained for random sea state represented by a P-M sea spectrum. The method involves a Van-Der-Pol transformation of the nonlinear equation of motion to convert it to the Ito’s stochastic differential equation with averaged drift and diffusion coefficients. The asymptotic stability in probability of the system is investigated by obtaining the averaged Ito’s equation for the Hamiltonian of the system. The asymptotic stability is examined approximately by investigating the asymptotic behaviour of the diffusion process Y(t) at its two boundaries Y = 0 and ∞. As an illustrative example, an articulated tower in a sea depth of 150 m is considered. The tower consists of hollow cylinder of varying diameter along the height, providing the required buoyancy of the system. Wave forces on the structure are calculated using Morrison’s equation. The stochastic response and the stability conditions are obtained for a sea state represented by P-M spectrum with 16m significant wave height. The results of the study indicate that the probability density of the stationary response obtained by the stochastic averaging procedure is in very good agreement with that obtained from digital simulation. Further, the articulated tower is found to be asymptotically stable under the parametric excitation arising due to hydrodynamic damping.

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