On Eigenvalue Sets and Convergence Rate of Itö Stochastic Systems with Markovian Switching
会议名称：《第二十九届中国控制会议》
会议日期：2010年
学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学]
基 金：The work of Bin Zhou and Zhao-Yan Li was partially supported by the National Natural Science Foundation of China under Grant Number60904007 the work of Bin Zhou was partially supported by the Development Program for Outstanding Young Teachers at Harbin Institute of Technology under Grant Number HITQNJS.2009.054 the work of Guang-RenDuan and Bin Zhou was partially supported by the Major Program of National Natural Science Foundation of China under Grant Number 60710002 the work of Yong Wang and Zhao-Yan Li was partially supported by the National Natural Science Foundations of China under Grant Number10771044 the Natural Science Foundation of Heilongjiang Province under Grant Number 200605
关 键 词：Time-delay Actuator saturation Parametric Lyapunov equation Nonlinear control Stabilization
摘 要：This paper is concerned with stability analysis and stabilization of Itö stochastic systems with Markovian switching.A couple of eigenvalue sets for some positive operator associated with the stochastic system under study are defined to characterize its stability in the mean square *** for these eigenvalue sets are established based on which we show that the spectral abscissa of these eigenvalues sets are the same and thus these eigenvalue sets are equivalent in the sense of characterizing the stability of the ***,it is shown that the guaranteed convergence rate of the Markovian jump Itö stochastic systems can be determined by some eigenvalue ***,a linear matrix inequality based approach is proposed to design controllers such that the closed-loop system has guaranteed convergence *** numerical examples are carried out to illustrate the effectiveness of the proposed *** research in this paper opens several perspectives for future work stated as some open problems.