Event-triggered filter of positive semi-Markovian jump systems with Weibull distribution

Abstract

This paper focuses on the event-triggered filter design of positive semi-Markovian jump systems with Weibull distribution. The considered systems are subject to random uncertainty and sensor fault. A linear programming-based filter design approach is proposed. First, an event-triggering condition is established by virtue of sensor output signals. Under the event-triggering condition, the filtering error system is transformed into an interval system. The positivity of the filtering error system is reached by considering the positivity of the lower bound of the interval system. By using a stochastic co-positive Lyapunov function, the filtering error system is stochastically stable with an ℓ1-gain performance by exploring the corresponding performance of the upper bound of the interval system. Then, additive and multiplicative models following the Bernoulli distribution are introduced to describe the random uncertainties of the systems. Consequently, the event-triggered filter is designed in terms of linear programming and a matrix decomposition approach. Moreover, the proposed filter design is developed for the systems subject to sensor faults. Finally, two examples are provided to illustrate the effectiveness of the proposed design.