Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

H∞ filtering for continuous fractional‐order 2D Roesser model: The 0<α≤1 case

“…It is obvious that (19) holds if and only if at least one of its terms is negative, that is to say H(, Λ • ) < 0 or H( * , Λ • ) < 0. From the definition of the stability region (4), Λ • ∈ 𝔚 C indicates that both H(, Λ • ) and H( * , Λ • ) are positive semidefinite, which contradicts (19). Therefore, Λ • is not in the region 𝔚 C , system (1) is proved to be stable.…”

“…The LMI‐based results of robust $$$ {H}_2,{H}_{\infty } $$$ problem and robust mixed $$$ {H}_2/{H}_{\infty } $$$ filtering are proposed in Tuan et al [18]. The $$$ {H}_{\infty } $$$ filtering problem of 2D continuous‐discrete Roesser systems with state‐delay in finite frequency domains is solved in Wang et al [19]. The bounded real lemmas and the $$$ {H}_{\infty } $$$ deconvolution filter design for the 2D digital system are derived in LMI form in Xie et al [20].…”

Robust Filtering for 2-D Systems With Uncertain-Variance Noises and Weighted Try-Once-Discard Protocols

“…To date, 2-D systems have already found successful applications in varieties of research fields ranging from image processing, chemical process, industrial automation to multivariable network visualization [2], [9]. Owing to its promising application prospects, 2-D system has been garnering a sizeable amount of research interests, and various issues in the 2-D case have been studied (see [4], [8], [10], [15], [29], [31], [38], [39], [44] and the references cited therein). It is worth mentioning that the state estimation or filtering problems for 2-D systems, which intend to extract the true signals based on the available measurements, have drawn particular research attention.…”