mathcal{H}_{infty} Filtering for Short-Time Switched Discrete-Time Linear Systems

In this paper, the $mathcal{H}_{infty}$ filtering problem for a class of short-time switched discrete-time linear systems is investigated. For such systems, switching always occurs in some short interval. Since the error state may attain large unacceptable values in short-time switching intervals, besides the asymptotic stability of error dynamics, the boundedness of error state is also significant for short-time switched systems. Thus the designed filter is composed of two parts: asymptotic filter, based upon the existing results, ensures the asymptotic stability of the system during normal, relatively long interval, and finite-time filter ensures system to be finite-time bounded during the short interval of switching, which is the main concern in this paper. By introducing the concept of finite-time boundedness, the proposed filter is formulated as a set of sub-filters ensuring the error dynamics $mathcal{H}_{infty}$ finite-time bounded in the short switching interval. Finally, a numerical example is provided to illustrate the effectiveness of this approach.