摘要
针对离散随机Markov跳跃系统,基于H表示方法研究了其对应的广义Lyapunov方程解的性质.首先,证明了广义Lyapunov方程存在唯一实对称矩阵序列解的充分必要条件是系统的谱不包含零特征值;然后,在系统的谱包含零特征值的情况下,分析了广义Lyapunov方程解的结构;最后,通过数值仿真表明了所得结论的正确性.
For discrete stochastic Markov jump systems, the properties of solutions to generalized Lyapunov equations(GLEs) are investigated based on the ?-representation method. Firstly, it is proved that the GLE has a unique solution in the form of a sequence of real symmetric matrices, if and only if the spectrum of the system does not contain zero eigenvalue. Moreover, the structure of solutions to GLEs is also discussed when there exist zero eigenvalue in the spectrum of the system. Finally, a numerical example is given to show the validity of the obtained results.
出处
《控制与决策》
EI
CSCD
北大核心
2014年第9期1693-1697,共5页
Control and Decision
基金
国家自然科学基金项目(61174078,61203053)
中国博士后基金项目(2013M531635)
山东省博士后创新项目专项资金项目(201203096)
教育部高等学校博士学科点专项基金项目(20120133120014)
山东省"泰山学者"建设工程专项经费项目