ABSTRACT

This paper is concerned with the stabilization problem for nonlinear stochastic delay systems with Markovian switching by feedback control based on discrete-time state and mode observations. By constructing an efficient Lyapunov functionals, we establish the sufficient stabilization criteria not only in the sense of exponential stability (both the mean-square stability and the almost sure stability) but also in other sense – that of $H_{\mathrm{\infty }}$ stability and asymptotic stability. Meanwhile, the upper bound on the duration τ between two consecutive state and mode observations is obtained. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.

摘要

本文关注基于离散时间状态和模式观测的反馈控制的马尔可夫切换非线性随机延迟系统的稳定问题。通过构造一个有效的 Lyapunov 泛函，我们不仅在指数稳定性（均方稳定性和几乎肯定稳定性）的意义上建立了充分的稳定标准，而且在其他意义上也建立了充分的稳定标准——$H_{\mathrm{\infty }}$稳定性和渐近稳定性。同时，获得了两个连续状态和模式观察之间的持续时间τ的上限。提供了数值例子来证明我们的理论结果的有效性。