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ℋ︁ ∞ filtering with secure eigenvalue calculation and precise integration
Author(s) -
Zhong W. X.,
Williams F. W.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19991110)46:7<1017::aid-nme737>3.0.co;2-i
Subject(s) - eigenvalues and eigenvectors , mathematics , rayleigh quotient , state vector , state variable , variable (mathematics) , variational principle , interval (graph theory) , norm (philosophy) , invariant (physics) , mathematical analysis , physics , mathematical physics , classical mechanics , quantum mechanics , combinatorics , law , thermodynamics , political science
Based on the analogy between structural mechanics and optimal control, interval mixed variable energy and the corresponding variational method are introduced to transform the induced norm γ of an ℋ ∞ filter into the fundamental eigenvalue γ −2 cr of a self‐adjoint operator, which can itself be expressed as a generalized Rayleigh quotient of the variational principle with two kinds of variable, i.e. the state vector x and the co‐state vector λ . These vectors correspond, respectively, to the displacement and internal force vectors in the theory of structural mechanics. The interval matrices Q , G and F of the mixed variable energy are introduced in a natural way, based upon which the precise integration of a time invariant system is proposed and then combined with the extended Wittrick–Williams algorithm to solve the eigen‐value problem, enabling the optimal eigenvalue parameter γ −2 cr to be computed with high precision. Copyright © 1999 John Wiley & Sons, Ltd.