带乘性噪声的非齐次Markov跳跃系统有限时间稳定性  

Finite-time stability for nonhomogeneous Markov jump systems with multiplicative noises

作　　者：周绍伟 陈兵[1] 刘洪霞 

机构地区：[1]青岛大学复杂性科学研究所,山东青岛266071 [2]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《控制与决策》2018年第3期565-570,共6页Control and Decision

基　　金：国家自然科学基金项目(61503224;61473160);山东省优秀中青年科学家科研奖励基金项目(BS2014SF005);山东省博士后创新项目专项资金项目(201403009);青岛市博士后应用研究项目;山东省高等学校优秀中青年骨干教师国际合作培养计划项目;山东科技大学科研创新团队支持计划项目(2015TDJH105)

摘　　要：研究一类带乘性噪声的离散时间非齐次随机Markov跳跃系统的有限时间稳定性,该系统的转移概率矩阵不是常矩阵而是区间矩阵.在区间矩阵紧性的假设下,将其表示为随机矩阵的凸组合.首先,给出系统有限时间稳定的充分必要条件;其次,利用Lyapunov方法和线性矩阵不等式技术得到系统有限时间稳定的充分条件,并用于设计有限时间状态反馈镇定控制器;最后,通过仿真算例说明所提出方法的有效性.The finite-time stability for a class of discrete-time stochastic Markov jump systems with multiplicative noises is studied. The transition probability matrix is not a constant matrix but a interval matrix. Under the assumption of the compactness of the interval matrix, it is represented as a convex combination of some random matrices. Firstly, the sufficient and necessary condition of finite-time stability is given. Then, a sufficient condition for the finite-time stability of the system is obtained and the finite-time stabilization controller with state feedback is designed by using the Lyapunov method and linear matrix inequality technique. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

关 键 词：非齐次Markov跳跃系统 区间转移概率矩阵 有限时间稳定 矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]