Stability and stabilization of a class of switched stochastic systems with saturation control  

作　　者：Yingxin GUO Shuzhi Sam GE Jianting FU Chao XU 

机构地区：[1]School of Mathematical Sciences,Qufu Normal University,Qufu 273165,China [2]Department of Electrical and Computer Engineering,National University of Singapore,Singapore 117576,Singapore [3]Chongqing Institutes of Green and Intelligent Technology,Chinese Academy of Sciences,Chongqing 400714,China [4]University of Chinese Academy of Sciences,Beijing 100049,China [5]Department of Control Science and Engineering,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China(Information Sciences)》2021年第12期143-155,共13页中国科学（信息科学）（英文版）

基　　金：supported by Natural Science Foundation of Shandong Province of China (Grant No. ZR2017MA045)。

摘　　要：A switching system always comprises of several subsystems and a rule supervising the switching between the subsystems. A major problem that is often inherent to all dynamical systems is actuator saturation. Saturation is a nonlinear property that nonlinearly maps small input signals to the output,which may affect the system properties and even destroy them. In this study, stability and stabilization of a class of switched stochastic systems with saturation control was investigated. First, the variation parameter method was used to present the integral form of switched stochastic systems. Second, to guarantee that the zero solution is globally exponentially stable in mean square, two sufficient conditions were obtained using direct computation with Gronwall inequality and indirect method with matrix theory, respectively. Further,another simple sufficient condition was obtained for the stability of the systems using the row norm, column norm, and Frobenius norm. Finally, two examples were used to illustrate the preciseness and effectiveness of the results. Moreover, various control designs were observed to stabilize the systems, which differ from the technique of linear matrix inequalities.

关 键 词：switched stochastic systems matric theory Gronwall inequality STABILITY 

分 类 号：O211.6[理学—概率论与数理统计] O231[理学—数学]