Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays
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摘要: 针对带马尔科夫跳的模态相关时变时滞系统得到了一个改进的均方指数稳定结果并设计了状态反馈控制器. 首先, 通过构造一个改进的Lyapunov-Krasovskii泛函, 以线性矩阵不等式的形式给出一个均方指数稳定性条件; 这里, 衰减率可以是一个在区间内取值的有限常数, 同时, 时变时滞的导数上界不要求小于1; 基于得到的稳定性条件, 设计了状态反馈的控制器. 最后, 通过两个仿真算例验证了所得理论的结果的有效性, 并与已有结果相比较, 保守性较弱.Abstract: In this paper, an improved mean-square exponential stability condition and delayed-state-feedback controller for stochastic Markovian jump systems with mode-dependent time-varying state delays are obtained. First, by constructing a modified Lyapunov-Krasovskii functional, a mean-square exponential stability condition for the above systems is presented in terms of linear matrix inequalities (LMIs). Here, the decay rate can be a finite positive constant in a range and the derivative of time-varying delays is only required to have an upper bound which is not required to be less than 1. Then, based on the proposed stability condition, a delayed-state-feedback controller is designed. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.
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Key words:
- Stochastic systems /
- time-varying delay /
- exponential stability /
- Markov chain
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