Adaptive event‐triggered fault detection for nonlinear positive semi‐Markov jump systems

Abstract

Summary This article investigates the asynchronous fault detection filter of nonlinear positive semi‐Markov jump systems with disturbances and actuator faults based on adaptive event‐triggering scheme. First, an adaptive event‐triggering strategy in the linear form is presented and a framework on the fault detection filter is established. Then, a hidden semi‐Markov model is introduced to describe the asynchronous phenomenon between the original system and the filter and thus an augmented fault detection system is constructed. Using stochastic Lyapunov functions and linear programming, the filter gains are determined for guaranteeing the positivity and stochastic stability with hybrid performance. Compared with existing results, the novelties of the proposed design lie in: (i) a new adaptive event‐triggered strategy is constructed, which improves the existing static one, (ii) an adaptive event‐triggered asynchronous filter is proposed for the underlying systems, (iii) hybrid gain performances of the filter are obtained with respect to the disturbance and fault, and (iv) a linear programming‐based computation method is given to determine the filter gains. Finally, one illustrate example is provided to verify the validity of the results in this article.