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Finite-time asynchronous control for positive discrete-time Markovian jump systems

Finite-time asynchronous control for positive discrete-time Markovian jump systems

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Finite-time asynchronous control problem is discussed for positive Markovian jump systems in this study. The non-synchronous behaviours generated between the system modes and controller modes are fully considered. To ensure the closed-loop system positivity and finite-time 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 age-structured population dynamic model.

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