This paper presents a refined complete multi-step delayed input and state estimation (MSDISE) by using the newly proposed system reformation approach, where a time-distributed unknown input filtering technique is used to facilitate the design. It is shown that within this new filtering approach, the optimal MSDISE can be readily achieved through the filters developed by Hsieh (2000) or Gillijns and De Moor (2007b). Asymptotic stability of the reformed state filter is explored for the corresponding time-invariant systems. Moreover, the relationships between the proposed asymptotic stability condition with those in literatures are also highlighted. A simulation example is given to show the effectiveness of the proposed results. (C) 2019 Elsevier Ltd. All rights reserved.
