【作者】 孙伟； 赵怡； 黄煜；

【Author】 SUN Wei, ZHAO Yi, HUANG Yu (School of Mathematics Computational Science, Sun Yet-san University, Guangzhou 510275, China.

【机构】 中山大学数学与计算科学学院；

【摘要】 研究线性无穷维切换系统的幂稳定性问题．给出两个幂稳定算子,对应两个线性子系统组成的离散线性无穷维切换系统的幂稳定性,应用离散系统的Lyapunov函数方法,找到两个系统的公共Lyapunov函数,从而得到此切换系统的幂稳定性的证明．比连续情况更加完善的地方是,不要求两个子系统对应的算子可交换．此方法可推广到有限个幂稳定算子的情况．更多还原

【Abstract】 It considers the problem of power stability of discrete linear switched infinite dimensional systems. For given two power stable operators, the corresponding conditions are obtained for power stability of discrete linear switched infinite dimensional systems with two linear subsystems. The Lyapunov function method is introduced to the discrete case which provides a common Lyapunov function for the two subsystem and leads to the proof of the results. This method is better than the continuous condition because the respective operators of the two subsystems needn’t be commuted which can be generalized to the switched systems with finite operators too.更多还原