Adaptive event-triggering distributed filter of positive Markovian jump systems based on disturbance observer.

This paper presents an adaptive event-triggered filter of positive Markovian jump systems based on disturbance observer. A new adaptive event-triggering mechanism is constructed for the systems. A positive disturbance observer is designed for the systems to estimate the disturbance. A distributed output model of each subsystem of positive Markovian jump systems is introduced. Then, an adaptive event-triggering distributed filter is designed by employing stochastic copositive Lyapunov functions. All presented conditions are solvable in terms of linear programming. Under the designed disturbance observer and the distributed filter, the corresponding error system is stochastically stable. The filter design approach is also developed for discrete-time positive Markovian jump systems. The contribution of the paper lies in that: (i) A new adaptive event-triggering mechanism is established for positive systems, (ii) A positive disturbance observer is designed for the disturbance of positive Markovian jump systems, and (iii) The designed distributed filter can guarantee the stochastic stability of the error while existing filters in literature only achieve the stochastic gain stability of the error. Finally, two examples are given to illustrate the effectiveness of the proposed design.