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Finitetime asynchronous control problem is discussed for positive Markovian jump systems in this study. The nonsynchronous behaviours generated between the system modes and controller modes are fully considered. To ensure the closedloop system positivity and finitetime boundedness with a guaranteed performance level, a sufficient condition on the existence of an asynchronous controller is first established by applying Lyapunov–Krasovskii functional approach and recursive matrix inequality methods. Then, with the aid of matrix conversions, the specific form of controller gain matrices can be constructed by solving linear matrix inequality (LMI) conditions. A numerical example is presented and application is illustrated to validate the proposed results by employing a pest's agestructured population dynamic model.
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