This paper is concerned with the self-triggered filtering problem for a class of Markovian jumping nonlinear stochastic systems. The event-triggered mechanism (ETM) is employed between the sensor and the filter to reduce unnecessary measurement transmission. Governed by the ETM, the measurement is transmitted to the filter as long as a predefined condition is satisfied. The purpose of the addressed problem is to synthesize a filter such that the dynamics of the filtering error is bounded in probability (BIP). A sufficient condition is first given to ensure the boundedness in probability of the filtering error dynamics, and the characterization of the desired filter gains is then realized by means of the feasibility of certain matrix inequalities. Furthermore, a self-triggered mechanism is designed to guarantee the filtering error dynamics to be BSP with excluded Zeno phenomenon. In the end, numerical simulation is carried out to illustrate the usefulness of the proposed self-triggered filtering algorithm.

本文涉及一类马尔可夫跳跃非线性随机系统的自触发滤波问题。在传感器和过滤器之间采用事件触发机制（ETM），以减少不必要的测量传输。由ETM进行控制，只要满足预定条件，就将测量结果传输到滤波器。解决的问题的目的是合成滤波器，以使滤波误差的动态性受概率（BIP）限制。首先给出充分的条件以确保滤波误差动态的概率的有界性，然后借助于某些矩阵不等式的可行性来实现所需滤波器增益的表征。此外，设计了一种自触发机制，以确保滤波误差动态为具有消除芝诺现象的BSP。最后，通过数值模拟来说明所提出的自触发滤波算法的有效性。