This article investigates the finite-time asynchronous control problem for continuous-time positive hidden Markov jump systems (HMJSs) by using the Takagi-Sugeno fuzzy model method. Different from the existing methods, the Markov jump systems under consideration are considered with the hidden Markov model in the continuous-time case, that is, the Markov model consists of the hidden state and the observed state. We aim to derive a suitable controller that depends on the observation mode which makes the closed-loop fuzzy HMJSs be stochastically finite-time bounded and positive, and fulfill the given L2 performance index. Applying the stochastic Lyapunov-Krasovskii functional (SLKF) methods, we establish sufficient conditions to obtain the finite-time state-feedback controller. Finally, a Lotka- Volterra population model is used to show the feasibility and validity of the main results.

中文翻译：

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基于T'模糊模型方法的连续时间正隐马尔可夫跳跃系统的有限时间L2增益异步控制


本文利用 Takagi-Sugeno 模糊模型方法研究了连续时间正隐马尔可夫跳跃系统 (HMJS) 的有限时间异步控制问题。与现有方法不同，所考虑的马尔可夫跳跃系统是用连续时间情况下的隐马尔可夫模型来考虑的，即马尔可夫模型由隐状态和观察状态组成。我们的目标是导出一个合适的控制器，该控制器取决于观察模式，使闭环模糊 HMJS 具有随机有限时间有界且为正值，并满足给定的 L2 性能指标。应用随机 Lyapunov-Krasovskii 泛函 (SLKF) 方法，我们建立了获得有限时间状态反馈控制器的充分条件。最后利用Lotka-Volterra群体模型验证了主要结果的可行性和有效性。