A Double Sensitive Fault Detection Filter for Positive Markovian Jump Systems with A Hybrid Event-Triggered Mechanism

This paper is concerned with the double sensitive fault detection filter for positive Markovian jump systems. A new hybrid adaptive event-triggered mechanism is proposed by introducing a non-monotonic adaptive law. A linear adaptive event-triggered threshold is established by virtue of 1-norm inequality. Under such a triggering strategy, the original system can be transformed into an interval uncertain system. By using a stochastic copositive Lyapunov function, an asynchronous fault detection filter is designed for positive Markovian jump systems (PMJSs) in terms of linear programming. The presented filter satisfies both <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{-}$</tex>-gain (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{-}$</tex>-gain) fault sensitivity and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{1}\ (\ell_{1})$</tex> internal differential privacy sensitivity. The proposed approach is also extended to the discrete-time case. Finally, two examples are provided to illustrate the effectiveness of the proposed design.