ABSTRACT
This chapter draws broadly the following conclusions: Traditional transfer function models of lumped linear time-invariant continuous time systems, despite their clarity of dynamics with poles and zeros, lead to nonlinear estimation. On the other hand linearly parameterized model structures simplify the problem, with linear estimation as the main advantage. Models parameterized with “Markov parameters” and “time moments” are basic forms- like power series representations of functions in general- which evolve into more versatile forms with Laguerre and Kautz functions as bases of expansions. Due to the linearity of the suggested parameterizations, the estimation is robust to zero-mean white/colored disturbances. The problem of inflated models for MIMO systems has been avoided since the chosen parameterizations do not involve unknown denominators. In robust estimations here the proposed https://www.w3.org/1998/Math/MathML"> ℋ ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429352850/bcdb6ac0-dd9f-41e6-a56b-f915f2a28a62/content/equ_993.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -norm bounded least squares algorithm is a special case of the set of https://www.w3.org/1998/Math/MathML"> ℋ ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429352850/bcdb6ac0-dd9f-41e6-a56b-f915f2a28a62/content/equ_993.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> filter equations. The https://www.w3.org/1998/Math/MathML"> ℋ ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429352850/bcdb6ac0-dd9f-41e6-a56b-f915f2a28a62/content/equ_993.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> -norm bounded LS estimator makes cautious information updates leading to active and accelerated estimation in the case of finite measurement data. On the whole this chapter takes a bird’s eye view of the entire book.
