In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwis...In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.展开更多
This note considers stability robustness bounds on a classof stochastic linear systems with delayed perturbations.Using the stochastic Lyapunov stability theory,severalsufficient conditions for delay-independent stoch...This note considers stability robustness bounds on a classof stochastic linear systems with delayed perturbations.Using the stochastic Lyapunov stability theory,severalsufficient conditions for delay-independent stochasticasymptotic stability are obtained.It is shown that if theperturbation terms satisfy some conditions,then the sto-chastic systems have the robustness.展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed tim...This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaptation law including the master-slave parame- ters are established for designing a delayed synchronization law in terms of linear matrix inequalities（LMIs）. The time-varying controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. Particularly, it is shown that the synchronization speed can be controlled by adjusting the updated gain of the synchronization signal. Two numerical examples are given to demonstrate the effectiveness of the method.展开更多
In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new...In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.展开更多
研究含有多面体参数摄动D e lta算子系统的鲁棒H∞滤波问题.基于D e lta算子系统有界实引理,提出了新的参数依赖型鲁棒H∞性能准则.利用该性能准则,采用线性矩阵不等式技术推导了此类系统全阶鲁棒H∞滤波器存在的充分条件,并通过求解一...研究含有多面体参数摄动D e lta算子系统的鲁棒H∞滤波问题.基于D e lta算子系统有界实引理,提出了新的参数依赖型鲁棒H∞性能准则.利用该性能准则,采用线性矩阵不等式技术推导了此类系统全阶鲁棒H∞滤波器存在的充分条件,并通过求解一个凸优化问题来设计滤波器.与基于二次稳定的滤波方案相比,该方法具有较小的保守性.最后以数值示例验证了所提出方法的可行性.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11771265).
文摘In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.
文摘This note considers stability robustness bounds on a classof stochastic linear systems with delayed perturbations.Using the stochastic Lyapunov stability theory,severalsufficient conditions for delay-independent stochasticasymptotic stability are obtained.It is shown that if theperturbation terms satisfy some conditions,then the sto-chastic systems have the robustness.
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
文摘This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaptation law including the master-slave parame- ters are established for designing a delayed synchronization law in terms of linear matrix inequalities（LMIs）. The time-varying controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. Particularly, it is shown that the synchronization speed can be controlled by adjusting the updated gain of the synchronization signal. Two numerical examples are given to demonstrate the effectiveness of the method.
文摘In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.
文摘研究含有多面体参数摄动D e lta算子系统的鲁棒H∞滤波问题.基于D e lta算子系统有界实引理,提出了新的参数依赖型鲁棒H∞性能准则.利用该性能准则,采用线性矩阵不等式技术推导了此类系统全阶鲁棒H∞滤波器存在的充分条件,并通过求解一个凸优化问题来设计滤波器.与基于二次稳定的滤波方案相比,该方法具有较小的保守性.最后以数值示例验证了所提出方法的可行性.
