A decentralized event-triggered mechanism to asynchronous observer design for stabilization of positive hidden Markov jump systems

This paper is focused on the network-based asynchronous positive observer design and stabilization of positive Markovian jump systems. To design the asynchronous positive observer, a novel distributed event-triggered mechanism, which differs from the quadratic form in normal systems, is proposed based on the network framework and relies on the output measurement. More importantly, different from recent literature that the observer design and the control issues of positive systems are studied separately due to technical concerns, this paper combined the two issues together and solved the problem of asynchronous observer gain matrix and asynchronous feedback gain matrix design. Under the availability of stochastic Markov Lyapunov functions, the positivity and stochastic stability of error dynamics and closed-loop systems are ensured by standard linear programming. Finally, a practical example is provided to demonstrate the effectiveness of the established method numerically.