H∞ filtering for discrete-time cyclic switched systems: Relaxed cycle-dependent persistent dwell-time constraints with averaging treatment

This note investigates the H_∞ filtering for a kind of discrete-time switched systems ruled by cyclic switching regularities. By virtue of the cyclic manipulation of dwell-time (DT) switching and average dwell-time (ADT) switching reported in the literature, an innovative switching strategy of cycle-dependent persistent dwell-time (CPDT) property is first developed referring to the original persistent dwell-time (PDT) scheme. Further, to overcome the cycle-dependent DT constraint appearing in the CPDT switching, cycle-dependent ADT is sub-regionally injected into the suffering areas, which is different from the full-regional injection of ADT into the PDT switching in the literature. In this way, the CPDT switching is advanced to the cycle-dependent average persistent dwell-time switching, which can bring more flexibility to the switching design. Based on the newly introduced switching mechanisms, quasi-time-dependent (QTD) stability and l₂-gain criteria are formulated for discrete-time cyclic switched systems to guide the design of intended QTD full-order filters, through which the produced filter error systems perform as expected in terms of the stability and H_∞ noise attenuation capability. At last, the validities and advantages of the obtained filtering solutions are expounded by specific illustrative examples.