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A note on persistency of excitation
We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the fullExpand
Overview of total least-squares methods
It is explained how special structure of the weight matrix and the data matrix can be exploited for efficient cost function and first derivative computation that allows to obtain computationally efficient solution methods. Expand
Low Rank Approximation - Algorithms, Implementation, Applications
  • I. Markovsky
  • Computer Science
  • Communications and Control Engineering
  • 3 August 2018
Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation and describes the applications including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation; computer vision for image deblurring and segmentation. Expand
Structured low-rank approximation and its applications
This work outlines applications in system theory (approximate realization, model reduction, output error, and errors-in-variables identification), signal processing, signal processing (harmonic retrieval, sum-of-damped exponentials, and finite impulse response modeling), and computer algebra (Approximate common divisor). Expand
Data-driven simulation and control
An approach for computing a linear quadratic tracking control signal that circumvents the identification step is presented and the results are derived assuming exact data and the simulated response or control input is constructed off-line. Expand
The element-wise weighted total least-squares problem
Modified total least-squares problem is formulated so that it provides a consistent estimator, i.e., the estimate [email protected]^ converges to the true value X"0 as the number of measurements increases. Expand
Identification of electrically stimulated muscle models of stroke patients
A review of existing modeling techniques with particular emphasis on their limitations is undertaken and a Hammerstein structure is selected and a suitable identification procedure and set of excitation inputs are developed to address these short-comings. Expand
Total least squares and errors-in-variables modeling
An overview of the progress of a modeling technique known as Total Least Squares in computational mathematics and engineering, and as Errors-InVariables (EIV) modeling or orthogonal regression in the statistical community is presented. Expand
Structured Low-Rank Approximation with Missing Data
This paper considers low-rank approximation of affinely structured matrices with missing elements, a singular linear least-norm problem, based on reformulation of the problem as inner and outer optimization. Expand
Algorithms for deterministic balanced subspace identification
It is shown that the computations can be performed on Hankel matrices of the input-output data of various dimensions and what is the optimal in terms of minimal identifiability condition partition of the data into ''past'' and ''future''. Expand