This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation an...This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.展开更多
Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approxi...Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.展开更多
The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for s...The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.展开更多
In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuou...In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical mean-square stability. A numerical example is exploited to show the vadlidness of the established results.展开更多
In this paper, the Holt’s exponential smoothing and Auto-Regressive Integrated Moving Average (ARIMA) models were used to forecast inflation rate of Zambia using the monthly consumer price index (CPI) data from May 2...In this paper, the Holt’s exponential smoothing and Auto-Regressive Integrated Moving Average (ARIMA) models were used to forecast inflation rate of Zambia using the monthly consumer price index (CPI) data from May 2010 to May 2014. Results show that the ARIMA ((12), 1, 0) is an adequate model which best fits the CPI time series data and is therefore suitable for forecasting CPI and subsequently the inflation rate. However, the choice of the Holt’s exponential smoothing is as good as an ARIMA model considering the smaller deviations in the mean absolute percentage error and mean square error. Moreover, the Holt’s exponential smoothing model is less complicated since you do not require specialised software to implement it as is the case for ARIMA models. The forecasted inflation rate for April and May, 2015 is 7.0 and 6.6 respectively.展开更多
The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constituti...The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.展开更多
We investigate the exponential stability in the mean square sense for the systems with Markovian switching and impulse effects.Based on the statistic property of the Markov process,a stability criterion is established...We investigate the exponential stability in the mean square sense for the systems with Markovian switching and impulse effects.Based on the statistic property of the Markov process,a stability criterion is established.Then,by the parameterizations via a family of auxiliary matrices,the dynamical output feedback controller can be solved via an LMI approach,which makes the closed-loop system exponentially stable.A numerical example is given to demonstrate the method.展开更多
In this paper, we find the ROC curves for Bi-Pareto and Bi-two parameter exponential distributions. Theoretical, parametric and non-parametric values of area under receiver operating characteristic (AUROC) curve for d...In this paper, we find the ROC curves for Bi-Pareto and Bi-two parameter exponential distributions. Theoretical, parametric and non-parametric values of area under receiver operating characteristic (AUROC) curve for different parametric combinations have been calculated using simulations. These values are compared in terms of root mean square and mean absolute errors. The results are demonstrated for two real data sets.展开更多
Background: Diabetic peripheral neuropathy (DPN) changes leg muscle coordination during walking and reduces stability. The aim of this study was to determine whether rhythmic auditory stimulation (RAS) affected the ga...Background: Diabetic peripheral neuropathy (DPN) changes leg muscle coordination during walking and reduces stability. The aim of this study was to determine whether rhythmic auditory stimulation (RAS) affected the gait performance of patients with DPN. Methods: Forty DPN patients (mean age, 59.1 ± 9.4 y) were randomly allocated to RAS and control groups in equal numbers. The participants in each group underwent 2 weeks of supervised rehabilitative treatment (40 min/day) as inpatients. This included walking twice a day, during which the RAS group participants walked in time with a metronome set at a self-chosen, comfortable rate. We compared gait function, lower limb muscle co-contraction, and gait stability before and after the intervention for both groups, calculated the change in score for each parameter, and assessed differences between the groups with unpaired t-tests and ANCOVA. Results: RAS was associated with significant improvement in all parameters. In the control group, there was no improvement in cadence, co-contraction, or gait stability (vertical). Compared with the control group, the RAS group showed improvement in co-contraction and gait stability. Conclusion: RAS may be helpful for improving the lower limb muscle coordination and gait function of DPN patients.展开更多
A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability crite...A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.展开更多
In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks （CRNNs） with stochastic delay. Different from the common assumptions on time delays,...In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks （CRNNs） with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique （the reciprocally convex combination method）, less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. Two numerical examples show that our results are better than the existing ones.展开更多
基金Supported by National Natural Science Foundation of China(10571036)the Key Discipline Development Program of Beijing Municipal Commission (XK100080537)
基金supported by the National Natural Science Foundation of China (No.60525303, 60604004, 60704009) Natural Science Foundationof Hebei Province, China (No.F2005000390, F2006000270)
文摘This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.
文摘Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.
文摘The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10771044)the Natural Science Foundation of Hunan Province(Grant No.09JJ6006)+2 种基金the Excellent Youth Foundation of Educational Committee of Hunan Provincial (Grant No.08B005)the Hunan Postdoctoral Scientific Pro-gram(Grant No.2009RS3020)the Scientific Research Funds of Hunan Provincial Education Department of China(Grant No.09C059)
文摘In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical mean-square stability. A numerical example is exploited to show the vadlidness of the established results.
文摘In this paper, the Holt’s exponential smoothing and Auto-Regressive Integrated Moving Average (ARIMA) models were used to forecast inflation rate of Zambia using the monthly consumer price index (CPI) data from May 2010 to May 2014. Results show that the ARIMA ((12), 1, 0) is an adequate model which best fits the CPI time series data and is therefore suitable for forecasting CPI and subsequently the inflation rate. However, the choice of the Holt’s exponential smoothing is as good as an ARIMA model considering the smaller deviations in the mean absolute percentage error and mean square error. Moreover, the Holt’s exponential smoothing model is less complicated since you do not require specialised software to implement it as is the case for ARIMA models. The forecasted inflation rate for April and May, 2015 is 7.0 and 6.6 respectively.
文摘The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.
基金supported by the National Natural Science Foundation of China(No.60974027)
文摘We investigate the exponential stability in the mean square sense for the systems with Markovian switching and impulse effects.Based on the statistic property of the Markov process,a stability criterion is established.Then,by the parameterizations via a family of auxiliary matrices,the dynamical output feedback controller can be solved via an LMI approach,which makes the closed-loop system exponentially stable.A numerical example is given to demonstrate the method.
文摘In this paper, we find the ROC curves for Bi-Pareto and Bi-two parameter exponential distributions. Theoretical, parametric and non-parametric values of area under receiver operating characteristic (AUROC) curve for different parametric combinations have been calculated using simulations. These values are compared in terms of root mean square and mean absolute errors. The results are demonstrated for two real data sets.
文摘Background: Diabetic peripheral neuropathy (DPN) changes leg muscle coordination during walking and reduces stability. The aim of this study was to determine whether rhythmic auditory stimulation (RAS) affected the gait performance of patients with DPN. Methods: Forty DPN patients (mean age, 59.1 ± 9.4 y) were randomly allocated to RAS and control groups in equal numbers. The participants in each group underwent 2 weeks of supervised rehabilitative treatment (40 min/day) as inpatients. This included walking twice a day, during which the RAS group participants walked in time with a metronome set at a self-chosen, comfortable rate. We compared gait function, lower limb muscle co-contraction, and gait stability before and after the intervention for both groups, calculated the change in score for each parameter, and assessed differences between the groups with unpaired t-tests and ANCOVA. Results: RAS was associated with significant improvement in all parameters. In the control group, there was no improvement in cadence, co-contraction, or gait stability (vertical). Compared with the control group, the RAS group showed improvement in co-contraction and gait stability. Conclusion: RAS may be helpful for improving the lower limb muscle coordination and gait function of DPN patients.
基金supported by NSFC (10871078)863 Program of China (2009AA044501)+1 种基金an Open Research Grant of the State Key Laboratory for Nonlinear Mechanics of CASGraduates' Innovation Fund of HUST (HF-08-02-2011-011)
文摘A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61273164,61034005,and 60974071)the National High Technology Research and Development Program of China(Grant No.2012AA040104)the Fundamental Research Funds for the Central Universities(Grant Nos.N100104102 and N110604007)
文摘In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks （CRNNs） with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique （the reciprocally convex combination method）, less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. Two numerical examples show that our results are better than the existing ones.
