This paper is concerned with H∞ filtering for a class of switched linear systems in discrete-time domain. A more general class of switching signals, the persistent dwell-time (PDT) switching is considered rather than the dwell-time or average dwell-time switching often studied in the literature. The concept on a stage of switching in the type of PDT switching signals is introduced, and each stage consists of a period of persistence and a dwell-time portion in which no switching occurs. A proper Lyapunov function suitable to the PDT switching is constructed, which is not only mode-dependent but also quasi-time-dependent (QTD). Then, a QTD filter is designed such that the resulting filtering error system is globally uniformly asymptotically stable and has a guaranteed H∞ noise attenuation performance. Certain techniques are explored such that the obtained performance index is of strictly non-weighted H∞ norm, which contrasts with the weighted (or called exponential) ones, i.e., weaker noise attenuation in the existing literature of switched systems with average dwell-time. An example of mass–spring system is provided to show the validity and potential of the developed results.