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Mixed H 2 /H ∞ filtering
Author(s) -
Khargonekar Pramod P.,
Rotea Mario A.,
Baeyens Enrique
Publication year - 1996
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199605)6:4<313::aid-rnc235>3.0.co;2-8
Subject(s) - kalman filter , mathematics , noise (video) , convex optimization , estimator , filtering problem , mathematical optimization , control theory (sociology) , matrix (chemical analysis) , optimization problem , computer science , algorithm , regular polygon , extended kalman filter , statistics , image (mathematics) , artificial intelligence , materials science , geometry , control (management) , composite material
In paper we consider the problem of finding a filter or estimator that minimizes a mixed H 2 /H ∞ filtering cost on the transfer matrix from a given noise input to the filtering error subject to an H ∞ constraint on the transfer matrix from a second noise input to the filtering error. This problem can be interpreted and motivated in many different ways; for instance, as a problem of optimal filtering in the presence of noise with fixed and known spectral characteristics subject to a bound on the filtering error due to a second noise source whose spectral characteristics are unknown. It is shown that one can come arbitrarily close to the optimal mixed H 2 /H ∞ filtering cost using a standard Kalman‐Luenberger estimator. Moreover, the problem of finding suitable Kalman‐Luenberger estimator gains can be converted into a convex optimization problem involving affine symmetric matrix inequalities.