This paper addresses the simultaneous interval estimations of actuator fault and sensor fault for a kind of discrete-time Markovian jump systems with generally bounded transition probabilities. It is worth noting that the generally bounded transition probability takes a more general form, thus having more realistic weight. The whole design process involves two steps, the first of which is to design an $L_{\infty }$ observer for robust estimations of faults, in view of its strong tolerance to faults. The second step is to develop a new interval estimation algorithm based on the zonotopic analysis, so as to get observer error ranges. The final interval estimations for actuator fault and sensor fault can be achieved by a combination of the robust $L_{\infty }$ observer with interval estimation algorithm. In the end, a circuit system is given to test the feasibility and advantage of the proposed method.

本文提出了一种具有一般有界转移概率的离散时间马尔可夫跳跃系统的执行器故障和传感器故障的同时区间估计。值得注意的是，一般有界转移概率采用更一般的形式，因此具有更现实的权重。整个设计过程包括两个步骤，第一步是设计一个${\mathrm{大号}}_{\infty }$鉴于其对故障的强大耐受性，因此可以对故障进行可靠的估计。第二步是基于区域局部分析开发一种新的区间估计算法，从而获得观察者误差范围。执行器故障和传感器故障的最终间隔估计可以通过结合鲁棒性来实现${\mathrm{大号}}_{\infty }$观察者与区间估计算法。最后，给出了一个电路系统来测试该方法的可行性和优势。