On the general decay stability of stochastic differential equations with unbounded delay

Xuejing Meng,Baojian Yin 대한수학회 2012 대한수학회지 Vol.49 No.3

This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is rst established to obtain the moment stability but with-out almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while ex-isting Razumikhin-type theorems aim at only the moment stability. By virtue of the M-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

ON THE GENERAL DECAY STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

Meng, Xuejing,Yin, Baojian Korean Mathematical Society 2012 대한수학회지 Vol.49 No.3

This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing Razumikhin-type theorems aim at only the moment stability. By virtue of the $M$-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

Almost Sure Stability of Dual Switching Continuous-time Nonlinear System With Deterministic and Stochastic Subsystems

Qian-qian Mu,Fei Long,Qi-xiang Wang,Lang Zhang,Li-po Mo 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1

In this paper, the almost surely globally asymptotical stability and the almost surely exponential stability for dual switching continuous-time nonlinear system are investigated by using the probability analysis method and stochastic Multi-Lyapunov function, respectively. Different from the previous research results, it is the first time that dual switching continuous-time nonlinear system is used as a study object to investigate its switching stability. Then, the probability analysis method is used to overcome the deficiency that the ergodicity no longer holds due to the variable transition rate of Markov process. Some sufficient conditions for the globally asymptomatic stability almost surely and the almost surely exponential stability of dual switching continuous-time nonlinear system are given under the pre-designed deterministic switching strategy. Finally, two numerical examples are provided to verify the effectiveness of the proposed approach.

동적 신뢰성 해석 기법의 수치 안정성에 관하여

이도근,옥승용 한국안전학회 2020 한국안전학회지 Vol.35 No.3

In comparison with the existing static reliability analysis methods, the dynamic reliability analysis(DyRA) method is more suitable for estimating the failure probability of a structure subjected to earthquake excitations because it can take into account the frequency characteristics and damping capacity of the structure. However, the DyRA is known to have an issue of numerical stability due to the uncertainty in random sampling of the earthquake excitations. In order to solve this numerical stability issue in the DyRA approach, this study proposed two earthquake-scale factors. The first factor is defined as the ratio of the first earthquake excitation over the maximum value of the remaining excitations, and the second factor is defined as the condition number of the matrix consisting of the earthquake excitations. Then, we have performed parametric studies of two factors on numerical stability of the DyRA method. In illustrative example, it was clearly confirmed that the two factors can be used to verify the numerical stability of the proposed DyRA method. However, there exists a difference between the two factors. The first factor showed some overlapping region between the stable results and the unstable results so that it requires some additional reliability analysis to guarantee the stability of the DyRA method. On the contrary, the second factor clearly distinguished the stable and unstable results of the DyRA method without any overlapping region. Therefore, the second factor can be said to be better than the first factor as the criterion to determine whether or not the proposed DyRA method guarantees its numerical stability. In addition, the accuracy of the numerical analysis results of the proposed DyRA has been verified in comparison with those of the existing first-order reliability method(FORM), Monte Carlo simulation(MCS) method and subset simulation method(SSM). The comparative results confirmed that the proposed DyRA method can provide accurate and reliable estimation of the structural failure probability while maintaining the superior numerical efficiency over the existing methods

기가빗 비디오 네트워크에서의 추계적 저전력 버퍼안정 라우팅

김중헌(Joongheon Kim),류은식(Eun-Seok Ryu) 한국방송·미디어공학회 2013 방송공학회논문지 Vol.18 No.3

This paper proposes a stochastic/dynamic routing protocol which aims the minimization of the summation of time average expected power expenditure with buffer stability in mobile ad-hoc 60 GHz wireless networks. By using 60 GHz RF, the wireless devices can transmit/receive 1080p HD video signals without compression. In addition, our algorithm works without centralized controller, so that the distributed operation is available. The novelty of the proposed algorithm was also verified by simulations.

Consensus Gain Conditions of Stochastic Multi-agent System with Communication Noise

Pingsong Ming,Jian-Chang Liu,Songhua Li 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.5

This paper investigates the consensus gain conditions of the stochastic multi-agent system (SMAS) withcommunication noise. A new consensus stability condition of the SMAS is given when the consensus gain functionc(t) does not satisfy the robustness condition of the consensus stability. Next we broaden the condition that theconsensus-gain function c(t) always must be positive, and obtain the sufficient condition of the SMAS’s consensusstability when the consensus-gain function c(t) is a negative constant. Finally, two simulation examples are givento illustrate the feasibility and effectiveness of the proposed results.

New Results on Finite-time Stabilization for Stochastic Systems with Time-varying Delay

Lihua Zhang,Wenhai Qi,Yonggui Kao,Xianwen Gao,Longjiang Zhao 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.2

The paper deals with the problem of finite-time stabilization for stochastic systems with time-varying delay by defining a new criterion for finite-time stability. Firstly, by use of more appropriate Lyapunov-Krasovskii functional (LKF), the difficulties of finite-time stability confronted in system analysis and synthesis can be overcome. Then, a state feedback controller is constructed to guarantee the closed-loop system finite-time stable. New conditions for finite-time stability analysis as well as controller synthesis are established in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the main results.

Stochastic Stability Analysis of the Power System Incorporating Wind Power using Measurement Wind Data

Panom Parinya,Anawach Sangswang,Krissanapong Kirtikara,Dhirayut Chenvidhya 대한전기학회 2018 Journal of Electrical Engineering & Technology Vol.13 No.3

This paper proposes an alternative method to evaluate the effect of wind power to the power system stability with small disturbance. Alternatively, available techniques for stability analysis of a power system based on deterministic methods are less accurate for high penetration of wind power. Numerical simulations of random behaviors are computationally expensive. A stochastic stability index (SSI) is proposed for the power system stability evaluation based on the theory of stochastic stability and energy function, specifically the stochastic derivative of the relative well-defined energy function and the critical energy. The SSI is implemented on the modified nine-bus system including wind turbines under different conditions. A doubly-fed induction generator (DFIG) wind turbine is characterized and modeled using measured wind data from several sites in Thailand. Each of the obtained wind power data is analyzed. The wind power effect is modeled considering the aggregated effect of wind turbines. With the proposed method, the system behavior is properly predicted and the stability is quantitatively evaluated with less computational effort compared with conventional numerical simulation methods.

Stochastic Stability Analysis of the Power System Incorporating Wind Power using Measurement Wind Data

Parinya, Panom,Sangswang, Anawach,Kirtikara, Krissanapong,Chenvidhya, Dhirayut The Korean Institute of Electrical Engineers 2018 Journal of Electrical Engineering & Technology Vol.13 No.3

This paper proposes an alternative method to evaluate the effect of wind power to the power system stability with small disturbance. Alternatively, available techniques for stability analysis of a power system based on deterministic methods are less accurate for high penetration of wind power. Numerical simulations of random behaviors are computationally expensive. A stochastic stability index (SSI) is proposed for the power system stability evaluation based on the theory of stochastic stability and energy function, specifically the stochastic derivative of the relative well-defined energy function and the critical energy. The SSI is implemented on the modified nine-bus system including wind turbines under different conditions. A doubly-fed induction generator (DFIG) wind turbine is characterized and modeled using measured wind data from several sites in Thailand. Each of the obtained wind power data is analyzed. The wind power effect is modeled considering the aggregated effect of wind turbines. With the proposed method, the system behavior is properly predicted and the stability is quantitatively evaluated with less computational effort compared with conventional numerical simulation methods.

Mean-square stability of two classes of theta Milstein methods for nonlinear stochastic differential equations

Mahmoud A. Eissa 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.1

Recently, there is growing interest in developing new numerical methods for stochastic dierential equations (SDEs), in order to improve the stability of approximation solution. There are many numerical methods have been constructed based on a Milstein scheme for SDEs. However, there exists very little results on the stability analysis of Milstein type methods for SDEs. This paper is concerned with mean-square (MS) stability of the semi-implicit theta Milstein methods and drifting split-step theta Milstein methods for nonlinear stochastic dierential equations. Under a coupled condition on the drifting and diusion coecients, it is proved that, the methods with > 1 2 are unconditionally preserve the MS-stability of the SDEs. For 2 [0; 1 2 ], the methods are MS-stable for some small step-size. This work is dierent from the previous works such that we could get rid of the restrictions that existed on the step-size of two classes Milstein methods for a symptomatic mean-square stability of the non-linear stochastic dierential equations, under Local lipschitz condition. Numerical experiments are given to demonstrate the conclusions.