This paper addresses the stability issue of switched linear systems with perturbed switching paths. First, by introducing the notions of child-path and parent-path, we are able to define the distance between two switc...This paper addresses the stability issue of switched linear systems with perturbed switching paths. First, by introducing the notions of child-path and parent-path, we are able to define the distance between two switching paths by means of their switching matrices chains. Next, we present the nice properties of the defined distance. Then, a stability criterion is presented for a class of switched linear systems with perturbed switching paths. Finally, an illustrative example is presented to verify the effectiveness of the approach.展开更多
In this paper, the following contaminated linear model is considered:y i=(1-ε)x τ iβ+z i, 1≤i≤n,where r.v.'s ｛ y i ｝ are contaminated with errors ｛ z i ｝. To assume that the errors have the fin...In this paper, the following contaminated linear model is considered:y i=(1-ε)x τ iβ+z i, 1≤i≤n,where r.v.'s ｛ y i ｝ are contaminated with errors ｛ z i ｝. To assume that the errors have the finite moment of order 2 only. The non parametric estimation of contaminated coefficient ε and regression parameter β are established, and the strong consistency and convergence rate almost surely of the estimators are obtained. A simulated example is also given to show the visual performance of the estimations.展开更多
This paper considers the estimation for a partly linear model with case 1 interval censored data.We assume that the error distribution belongs to a known family of scale distributions with an unknown scaleparameter. T...This paper considers the estimation for a partly linear model with case 1 interval censored data.We assume that the error distribution belongs to a known family of scale distributions with an unknown scaleparameter. The sieve maximum likelihood estimator (MLE) for the model's parameter is shown to be stronglyconsistent, and the convergence rate of the estimator is obtained and discussed.展开更多
This paper presents the isogeometric least-squares collocatio method,which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense....This paper presents the isogeometric least-squares collocatio method,which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense.The number of collocation points employed in IGA-L can be larger than that of the unknowns.Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods.First,a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution.Second,IGA-L method is more flexible and more stable,because the number of collocation points in IGA-L is variable.Third,IGA-L is convergent in some cases of singular parameterization.Moreover,the consistency and convergence analysis are also developed in this paper.展开更多
基金This work was partially supported by the National Natural Science Foundation of China (No. 60428304).
文摘This paper addresses the stability issue of switched linear systems with perturbed switching paths. First, by introducing the notions of child-path and parent-path, we are able to define the distance between two switching paths by means of their switching matrices chains. Next, we present the nice properties of the defined distance. Then, a stability criterion is presented for a class of switched linear systems with perturbed switching paths. Finally, an illustrative example is presented to verify the effectiveness of the approach.
文摘In this paper, the following contaminated linear model is considered:y i=(1-ε)x τ iβ+z i, 1≤i≤n,where r.v.'s ｛ y i ｝ are contaminated with errors ｛ z i ｝. To assume that the errors have the finite moment of order 2 only. The non parametric estimation of contaminated coefficient ε and regression parameter β are established, and the strong consistency and convergence rate almost surely of the estimators are obtained. A simulated example is also given to show the visual performance of the estimations.
基金the National Natural Science Foundation of China(Grant No. 19631040).
文摘This paper considers the estimation for a partly linear model with case 1 interval censored data.We assume that the error distribution belongs to a known family of scale distributions with an unknown scaleparameter. The sieve maximum likelihood estimator (MLE) for the model's parameter is shown to be stronglyconsistent, and the convergence rate of the estimator is obtained and discussed.
基金supported by the National Natural Science Foundation of China under Grant No.61872316the Natural Science Foundation of Zhejiang Province under Grant No.LY19F020004。
文摘This paper presents the isogeometric least-squares collocatio method,which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense.The number of collocation points employed in IGA-L can be larger than that of the unknowns.Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods.First,a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution.Second,IGA-L method is more flexible and more stable,because the number of collocation points in IGA-L is variable.Third,IGA-L is convergent in some cases of singular parameterization.Moreover,the consistency and convergence analysis are also developed in this paper.
