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

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

作者机构：School of Mathematical SciencesQufu Normal University Department of Electrical and Computer EngineeringNational University of Singapore Chongqing Institutes of Green and Intelligent TechnologyChinese Academy of Sciences University of Chinese Academy of Sciences Department of Control Science and EngineeringZhejiang University 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2021年第64卷第12期

页      面：147-159页

核心收录：

学科分类：02[经济学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 070103[理学-概率论与数理统计] 071101[理学-系统理论] 0711[理学-系统科学] 0202[经济学-应用经济学] 020208[经济学-统计学] 0714[理学-统计学（可授理学、经济学学位）] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

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

主　　题：switched stochastic systems matric theory Gronwall inequality stability 

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.