具有外部扰动的线性离散系统有限时间有界性

对于外部扰动满足一个动态方程的线性离散系统,通过构造一个不含外部扰动项的李雅普诺夫函数,给出了此类系统有限时间有界的充分条件,与现有结果相比,该充分条件可以降低保守性.在此基础上,分别讨论了此类系统有限时间有界状态反馈控制器以及输出反馈控制器存在的充分条件.这些条件都可以转换为线性矩阵不等式的可行性问题.最后,通过仿真实验验证了本方案的有效性.

Finite-time boundedness of discrete-time linear systems with exogenous disturbances

A new Lyapunov function was constructed without the term of disturbances,and some sufficient conditions were given for finite-time boundedness for a class of discrete-time systems with exogenous disturbances.The disturbances were generated by an exosystem.Compared with the existed results,these conditions can decrease the conservation.Some sufficient conditions for the existence of state feedback controller and output feedback controller were also given.These conditions can be reduced to feasibility problems involving linear matrix inequalitie(LMI).Finally,the proposed methodology was illustrated by an example.