A Novel Short Time H∞ Filtering for Discrete Linear Systems

In this paper, a novel short time $\mathrm{H}\infty$ filtering methods is proposed for discrete linear systems. Firstly, a novel $\mathbf{H}\infty$ filtering performance criterion is given in a finite time window. Secondly, a sufficient condition to fulfill the given performance criterion function is deduced, and the short time $\mathbf{H}\infty$ filter is obtained through solving a linear matrix inequality (LMI). The obtained short time $\mathbf{H}\infty$ filter need not assume that the energy of the system noise is bounded for the whole time domain, which is more usual in practical applications. What's more, the filtering parameters can be changed with the system real-time running condition. The simulation illustrates the feasibility and effectiveness of the short time $\mathbf{H}\infty$ filters.