A reduced-order deconvolution filter design using bounded real lemma

H∞ Deconvolution Filters for Stochastic Systems with Interval Uncertainties

“…✷ Remark 2. In Theorem 1, it was shown that the transmission channel with stochastic disturbances and interval uncertainties is stochastically stable with the disturbance attenuation level γ if two LMIs (13) and (14) are feasible, and the H ∞ deconvolution filter can be designed based on (15). Note that, by using the MATLAB LMI Toolbox, the feasibility of the LMIs (13) and (14) can be checked easily.…”

“…Therefore, how to solve the deconvolution problem has become an interesting and important topic in signal processing. Considerable attention has been devoted to the analysis and design of many kinds of deconvolution filters and much literature has appeared on the topic in the past ten years; see, e.g., [2], [3], [7], [12], [13], [14], [20].…”

“…The robust stability, stabilization, control, and filtering problems for stochastic systems have been intensively investigated by many researchers, and many results on these topics have been reported in the literature; see, e.g., [7], [18], [19]. The H ∞ disturbance rejection level is a well-known important criterion for quantifying the system performances, and has been widely used in studying robust control and signal processing problems for deterministic and stochastic systems; see, e.g., [4]- [6], [13]- [16], [18], [19], [21]. Also, the H ∞ deconvolution filter design problem has been investigated for deterministic and stochastic systems; see [13], [14], [20] for some recent publications.…”

“…The H ∞ disturbance rejection level is a well-known important criterion for quantifying the system performances, and has been widely used in studying robust control and signal processing problems for deterministic and stochastic systems; see, e.g., [4]- [6], [13]- [16], [18], [19], [21]. Also, the H ∞ deconvolution filter design problem has been investigated for deterministic and stochastic systems; see [13], [14], [20] for some recent publications. However, to the best of the authors' knowledge, the robust H ∞ deconvolution filtering problem for stochastic systems with interval uncertainties has not been dealt with yet and remains an interesting topic.…”

H∞ deconvolution filter design for uncertain descriptor hybrid delay systems with limited communication capacity and unknown transition rates

“…Conversely, H 1 deconvolution filtering is to design a filter to estimate the unknown input signal of a given systems utilizing available measurement [41][42][43][44]. Over the past decades, as the extension of H 1 filtering, H 1 deconvolution filtering has been an important issue and widely used in many fields such as signal processing, image restoration, data transmission, nondestructive evaluation, reverberation cancellation, and so on [45][46][47][48].…”