Quasi-Time-Dependent $${\mathscr {H}}_\infty $$ H ∞ Filtering of Discrete-Time 2-D Switched Systems with Mode-Dependent Persistent Dwell-Time

In this paper, a quasi-time-dependent (QTD) $${\mathscr {H}}_\infty $$ filtering approach to discrete-time two-dimensional switched systems is presented, by applying the mode-dependent persistent dwell-time (MPDT) switching method. The Fornasini–Marchesini local state-space model is used to describe the interested system. Compared with the dwell-time and the average dwell-time switchings which are often used in the literature, a MPDT switching, which is a more general class of switching form, is studied in this paper. The objective is to design a full-order filter that ensures the filtering error system exponentially stable with a guaranteed $${\mathscr {H}}_\infty $$ noise attenuation performance. By constructing a QTD switched Lyapunov-like function, the sufficient conditions for the existence of the filter are established by using the MPDT switching. The time-independent filter is actually a special case of QTD filter studied in this paper, which implies the developed results in this paper are more general with less conservativeness. Finally, two numerical examples are showed to validate the effectiveness and potential of the developed filter design method.