H-infinity filtering with secure eigenvalue calculation and precise integration

Based on the analogy between structural mechanics and optimal control, inte rval mixed variable energy and the corresponding variational method are int roduced to transform the induced norm gamma of an H-infinity filter into th e fundamental eigenvalue gamma(cr)(-2) of a self-adjoint operator, which ca n 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-s tate vector lambda. These vectors correspond, respectively, to the displace ment 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 invarian t system is proposed and then combined with the extended Wittrick-Williams algorithm to solve the eigenvalue problem, enabling the optimal eigenvalue parameter gamma(cr)(-2) to be computed with high precision. Copyright (C) 1 999 John Wiley & Sons, Ltd.