Robust passivity analysis of Markov‐type Lotka–Volterra model with time‐varying delay and uncertain mode transition rates
Robust passivity analysis of Markov‐type Lotka–Volterra model with time‐varying delay and uncertain mode transition rates
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DOI：
10.1002/mma.6447
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发表时间：
2020-04
影响因子：
2.9
通讯作者：
Lan Wang;Yiping Dong;Da Xie;Jinde Cao
中科院分区：
文献类型：
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作者：
Lan Wang;Yiping Dong;Da Xie;Jinde Cao
研究了一类具有时变时滞的新型马尔可夫切换Lotka-Volterra （LV）模型的全局鲁棒无源性问题。首先将模式转换速率不确定的马尔可夫切换引入到捕食系统的建模中，并对模型参数的不确定性进行了充分的讨论，能够体现出现实的实际意义。利用无源性理论和不等式技术研究了具有扰动输入和反馈控制的不确定LV模型的鲁棒无源性。利用Lyapunov-Krasovskii泛函导出了充分的判据，并设计了相应的控制器以保证闭环不确定LV模型的无源性。最后，给出了一个三种双模LV模型来说明所提理论结果的有效性。
This paper devotes to the global robust passivity problem for a novel Markovian switching Lotka–Volterra (LV) model with time‐varying delay. The Markovian switching with uncertain mode transition rates is first drawn into modeling the predator–prey system and the uncertainty of model parameters is also fully discussed, which can reflect the realistic practical significance. The robust passivity for the uncertain LV model with disturbance input and feedback control is studied by the passivity theories and inequality techniques. Some sufficient criteria are derived by the Lyapunov–Krasovskii functional, and the corresponding controllers are designed to ensure the passivity of the proposed closed‐loop uncertain LV model. Finally, a three‐specie two‐mode LV model is provided to illustrate effectiveness of the proposed theoretical results.