This paper proposes the use of regularization on the multivariable formulation of the Virtual Reference Feedback Tuning (VRFT). When the process to be controlled has a significant amount of noise, the standard VRFT approach, that uses the instrumental variable technique, provides estimates with very poor statistical properties. To cope with that, this paper considers the use of regularization on the estimation procedure, reducing the covariance error at the cost of inserting a small bias. Also, this paper explains different types of regularization matrices and presents the methodology to tune these matrices. In order to demonstrate the benefits of the proposed formulation, a numerical example is presented.

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The dynamic physical interval where postmortem alteration of biological remains takes place is widely known as the taphonomically active zone (TAZ). In benthic systems, the TAZ is conventionally considered to be delimited by an upper boundary at the sediment-water interface and a lower boundary corresponding roughly to the deepest sediment layer influenced by bioturbation. However, this definition was developed in the context of marine or continental environments inhabited by benthic fauna and disregards the modifications that pelagic remains undergo while sinking through the water column. Indeed, long before the skeletal remains of planktonic organisms reach the sediment-water interface, they may suffer significant taphonomic damage, primarily due to dissolution. The magnitude of dissolution depends on the composition of the skeletal remains, seawater properties, and the nature and intensity of biological processes in the water column. In open ocean environments, siliceous remains (e.g., diatoms, radiolarians) suffer enhanced dissolution in the upper water column, where seawater is undersaturated in silica, whereas pelagic carbonate remains (e.g., foraminifers, coccolithophores) experience higher dissolution below the lysocline (the depth where there is a sharp increase in dissolution rate) until they reach the carbonate compensation depth (CCD), where dissolution is complete. Therefore, we argue that the TAZ concept for pelagic organisms should be extended to include the water column through which they settle after death. Furthermore, the extent of taphonomic damage of pelagic microfossils can be used as a potential proxy for past changes in seawater chemistry and circulation related to oceanographic conditions. © 2018, SEPM (Society for Sedimentary Geology).