在离散观测和反馈延迟下的混杂随机系统镇定（英文）

Stabilisation of hybrid stochastic systems under discrete observation and sample delay

对混杂随机系统的状态反馈控制近年来引起了广泛的关注.一个更现实也更经济的情况是对状态的观测不是连续时间而是离散时间的.同时,现实中绝大多数的观测和反馈系统都或多或少会存在时滞现象.因此,讨论这种基于离散时间观测同时带有观测反馈时滞的混杂随机系统的反馈控制是很有意义的.特别地,通过使用一个李雅普诺夫泛函,不仅可以得到H无穷稳定、渐近稳定和指数稳定,而且还能显著地改善对时滞上界的要求.本文是文献[20]工作的深入和推广.

State feedback controls for hybrid stochastic differential equations have attracted lots of attention in recent years. It is more economic and practical that the states are observed at discrete time instead of continuous time. In addition,most observations and feedback systems have some time delays in practice. Therefore, it is interesting to investigate feedback controls based on discrete-time observations with sample delays for hybrid systems. In this paper, exponential stabilisations both in H1 and asymptotical sense are discussed using Lyapunov functionals. The upper bound of the delay time is also improved. This work is devoted as a continuous research to Ref. [20].