Sampled-data-based dynamic event-triggered asynchronous control of continuous-time positive Markov jump systems

The L1-gain asynchronous control issue of continuous-time positive Markov jump systems has been investigated using an event-triggered method. First, in light of positivity and Zeno behavior, a linear programming dynamic event-triggered method based on sampled data is introduced to regulate the data sending from system feedback state to the controller, which can eliminate Zeno behavior and reduce the network resources occupied by frequent data sending. Since the controller does not receive the system mode information accurately, the asynchronous phenomenon is taken into account via a hidden Markov model. Through the introduction of auxiliary variables and the development of a novel co-positive Lyapunov functional, the positivity of the closed-loop positive Markov jump systems is examined, and the stability condition is achieved. Then, a cooperative design scheme between a desired sampled-data-based dynamic event-triggered L1-gain asynchronous controller and the sampled-data-based dynamic event-triggered method is formulated. Finally, a numerical example shows the effectiveness of this work in this paper. •For PMJSs, a more versatile sampled-data-based dynamic ETM in LP-form is suggested, which not only outperforms the static one in terms of resource use but also avoids Zeno behavior and enables the construction of co-positive Lyapunov functional to achieve less conservative conditions.•By introducing auxiliary variables, the positivity of PMJSs is studied in the context of sampled-data-based dynamic ETM designed in this paper.•Considering the role of sampling on the system stability, a co-positive Lyapunov functional with looped functions is developed, and the solvability criterion of related problem is given. Meanwhile, a desired sampled-data-based DETAC and the sampled-data-based dynamic ETM are designed in cooperation.•Furthermore, for the proposed ETM, the influence of different parameters on the average data sent is discussed in numerical example.