\(H_\infty\) filtering for discrete-time cyclic switched systems: relaxed cycle-dependent persistent dwell-time constraints with averaging treatment. (English) Zbl 1533.93163
Summary: This note investigates the \(H_\infty\) 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 \(l_2\)-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 \(H_\infty\) noise attenuation capability. At last, the validities and advantages of the obtained filtering solutions are expounded by specific illustrative examples.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93E11 | Filtering in stochastic control theory |
| 93C55 | Discrete-time control/observation systems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
Keywords:
\(H_\infty\) filtering; cycle-dependent persistent dwell-time; cycle-dependent average persistent dwell-time; discrete-time cyclic switched systems; stability and \(l_2\)-gainReferences:
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