H∞ deconvolution filter design for uncertain linear discrete time-variant systems: A Krein space approach

Abstract

This paper aims to investigate the problem of deconvolution filter design for linear discrete time-variant dynamic systems subject to energy bounded disturbance, online known controlled input and modelling errors. In order to construct such a filter without introducing conservatism, a new-defined performance criterion is given as a substitution of the conventional H∞ performance index by carefully taking these uncertainties into account, and the concerned problem is reformulated as a two-step optimization issue of searching out the positive minimal value of the alternative criterion within a dynamic constraint. Through appropriately defining a set of stochastic variables that belong to an indefinite inner product space, an artificial Krein space model is introduced. In paralleling with the white noise estimation techniques in Hilbert space, the orthogonal projection theory is employed to tackle with the reformulated problem. An existence condition of the filter is explicitly derived and its gain matrix is obtained in a recursive form which benefits real-time implementation. To exhibit the validity of the addressed methodology for estimating exogenous input and fault signal in dynamic systems, two examples are bestowed.