Asynchronous positive filter design for switched positive systems with overlapped detection delay

A novel approach to L1 filter design for asynchronously switched positive linear systems with dwell time

“…Can we design the asynchronous filter gains individually to improve the performance of the closed‐loop system? Furthermore, it is also found that the energy functions are always prohibited to increase in the work of Li and Zhang, whereas in other works, the energy functions are allowed to increase during the unmatched interval or at the switching instants. Can the two classes of energy functions be unified to make the results more comprehensive?…”

“…Many results on the L 1 ‐gain analysis and synthesis problems of switched positive systems have been obtained. To mention a few, the L 1 ‐gain performance of switched positive singular systems with delays has been studied in the work of Li and Lin, the stability and L 1 ‐gain performance of switched positive linear systems (SPLSs) have been studied in the work of Xiang et al, and the robust stability and L 1 ‐gain performance of switched positive fuzzy systems have been investigated in the work of Li et al The readers can refer to the literature for further results.…”

“…The weighted L 1 control problem for continuous‐time asynchronously SPLSs with delays has been addressed in the work of Xiang et al The nonweighted L 1 control problem for continuous‐ and discrete‐time asynchronously SPLSs with dwell time has been studied in the work of Li and Zhang . The asynchronous nonweighted L 1 filter problem of discrete‐time SPLSs with dwell time has been investigated in the work of Ren et al As far as we know, the asynchronous filtering problem of continuous‐time SPLSs has not been studied yet, and in the aforementioned literature, it is noted that the controller/filter gains will continue to be used when modes of the filter and subsystem are unmatched. This will no doubt increase the conservativeness of the results.…”

“…Compared with the literature, the contributions of this paper are shown as follows. Unlike existing works concerned with asynchronous problems of SPLSs, the asynchronous and synchronous filters are designed separately, which lowers the conservatism of the results. Unlike existing works concerned with asynchronous control or filtering problems, we construct a novel clock‐dependent Lyapunov function (CDLF), which may increase when the modes of the filter and subsystem are unmatched, or keeps decreasing all the time, and jumps down when the filter or subsystem switches. We also explore that whether allowing the increase of CDLF during asynchronous interval implies less conservative results. By using the CDLFs approach, sufficient conditions characterizing a nonweighted L 1 performance are derived for the filtering error systems. Based on the L 1 analysis results, sufficient conditions are established to check the existence of a pair of error‐bounding filters, which can estimate the outputs of the system in real time under a nonweighted L 1 performance. …”

Weighted‐average ℓ1 filtering for switched positive systems

“…Under the constraint of state‐dependent switching, stability and ‐gain performance are established for delayed positive switched systems in . Further stability results for such systems can be found in and references therein. The sufficient conditions for checking the existence of estimator are provided for discrete‐time switched positive linear systems in .…”