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主要研究了具有输入时滞和乘性噪声的离散时间随机系统渐近均方镇定性问题。首先,基于Lyapunov不等式,给出易于验证的系统渐近均方镇定性的充分条件。其次,基于耦合Lyapunov方程,得到系统渐近均方镇定性的必要性条件。值得注意的是,当所研究系统退化为无时滞随机系统或确定性时滞系统,系统的渐近均方镇定性等价于耦合Lyapunov方程解的存在唯一性。
The problem of asymptotically mean square stabilization of discrete-time stochastic systems with input delay and multiplicative noise is mainly studied. First, based on the Lyapunov inequality, sufficient conditions for the asymptotically mean square stabilization of the system are given. Secondly, based on the coupled Lyapunov equation, the necessary conditions for the asymptotic mean square stabilization of the system are obtained. It is worth noting that the asymptotically mean square stability of the system is equivalent to the existence and uniqueness of the solution of the coupled Lyapunov equation when the system under study is degenerated into a stochastic system with no delay or a deterministic time-delay system.