Abstract: Based on the linear matrix inequality and slack variable, the finite-time stability and filtering problems for discrete-time piecewise impulsive system are investigated. On one hand, the sufficient conditions are given for the filter error system which is finite-time stable and meets the performance requirement. On the other hand, the sufficient conditions for solving the finite-time filter problem are also obtained, and the design method of filter is presented. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the conclusion.

Key words: finite-time stability, finite-time filtering, impulsive system, discrete-time system

摘要： 利用线性矩阵不等式和松弛变量方法，研究了离散时间分段脉冲系统的有限时间稳定和滤波问题。一方面给出了滤波误差系统有限时间稳定和满足性能要求的充分条件。另一方面也给出了有限时间滤波问题可解的充分条件和滤波器的设计方法。最后通过数值算例表明了结论的可行性和有效性。

关键词: 有限时间稳定, 有限时间滤波, 脉冲系统, 离散时间系统