Event‐triggered positive <i>L</i><sub>1</sub> filter design for positive Markovian jump systems with quantization
Di Zhang, Baozhu Du, Yuanwei Jing
Abstract
Abstract This paper is concerned with the design of positive filter for positive Markovian jump systems (PMJSs) with adaptive event‐triggered mechanism and quantization. Considering the mode jump of the system, a new adaptive event‐triggered condition is established, which not only can regulate the communication threshold according to the error of dynamic systems, but also can avoid the asynchronous phenomenon between the system mode and the filter mode. In order to further reduce the burden of communication, a new positive filter with the quantized measure system output is developed, and the design condition which ensures the filter error system to be stochastically stable with performance is presented which can be solved in terms of linear programming (LP) technique. It is illustrated that there is no Zeno phenomenon. The proposed results are applied to the power allocation in a mobile telecommunication system, and it is shown that compared with the existing results, the event‐triggered filter of this paper has some advantages.