In this work, the problem of $L_{\infty }$-gain filtering of semi-Markov jump systems (S-MJSs) subjected to persistent bounded disturbances is investigated. We first provide a sufficient condition for input-to-state stability (ISS) of the systems under consideration. The analytical result of ISS is then recast as a linear matrix inequality (LMI) feasibility problem by using the S-procedure. Based on the ISS analysis, a novel $L_{\infty }$-gain filter design scheme is developed. The resulting filter ensures the trajectories of the estimation error at steady state to be bounded in the mean sense and makes the peak of the estimation error as small as possible under the effect of the external disturbances. Simulation results demonstrate the effectiveness of our proposed design scheme.

在这项工作中，问题${\mathrm{大号}}_{\infty }$研究了遭受持续有界扰动的半马尔可夫跳跃系统（S-MJS）的增益滤波。我们首先为所考虑系统的输入到状态稳定性（ISS）提供充分条件。ISS 的分析结果然后通过使用 S 过程重新转换为线性矩阵不等式 (LMI) 可行性问题。基于 ISS 分析，小说${\mathrm{大号}}_{\infty }$- 开发了增益滤波器设计方案。由此产生的滤波器保证了稳态时估计误差的轨迹在平均意义上是有界的，并使估计误差的峰值在外部干扰的影响下尽可能小。仿真结果证明了我们提出的设计方案的有效性。