Robust Filtering for Linear Time-Invariant Continuous Systems

• Published in: IEEE transactions on signal processing Vol. 55; no. 10; pp. 4752 - 4757
• Main Authors: Neveux, P., Blanco, E., Thomas, G.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Continuous time systems; Detection, estimation, filtering, equalization, prediction; Diophantine equation; Electric power; Engineering Sciences; Equations; Estimation error; Estimators; Exact sciences and technology; Filtering; Filtration; Information, signal and communications theory; Mathematical models; minimax optimization; Miscellaneous; Nonlinear filters; Polynomials; Representations; robust estimation; Robustness; sensitivity; Signal and communications theory; Signal processing; Signal, noise; Spectra; spectral factorization; State estimation; Telecommunications and information theory; Transfer functions; Uncertainty; Estimation error; Filtering; Diophantine equation; Robust estimation; Factorization; Optimization; Robust control; Time invariance; minimax optimization; Minimax method; Signal processing; Robustness; spectral factorization; sensitivity; Causality; Transfer function; Continuous system; polynomial matrices; optimisation; matrix decomposition; signal processing; filtering theory; transfer function matrices
• DOI: 10.1109/TSP.2007.896104
• ISSN: 1053-587X

The problem of robust filtering for linear time-invariant (LTI) continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations, and then in the state-space domain. The basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv-contaminated model. The general solution to the problem is given in the transfer function representation while, in the polynomial framework, the causal estimator is obtained by means of a spectral factorization and a Diophantine equation. The state-space realization of the causal estimator is discussed. Examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty.