ABSTRACT
One of the fundamental problems of signal and systems theory is the estimation of state-variables of a dynamic system (filtering) using available (past) noisy measurements. The celebrated Kalman filtering approach [3,4] is, by now, deeply entrenched in the control literature and offers the best filter algorithm based on the minimization of the variance of the estimation error. This type of estimation relies on knowledge of a perfect dynamic model for the signal generation system and the fact that power spectral density of the noise is known. In many cases, however, only an approximate model of the system is available. In such situations, it has been known that the standard Kalman filtering methods fail to provide a guaranteed performance in the sense of the error variance. Considerable interests have been subsequently devoted to the design of estimators that provide an upper bound to the error variance for any allowable modeling uncertainty [10-12,14-17]. These filters are referred to as robust filters and can be regarded as an extension of the standard Kalman filter to the case of uncertain systems. An important class of robust filters is the one that employs the H∞ – norm as a performance measure. In H∞ – filtering, the noise sources are arbitrary signals with bounded energy which is appropriate when there is significant uncertainty in the power spectral density of the exogenous signals [18].
