Contents I. Introduction
The problems of estimation and filter design have received much attention in the past decades. It is known that one of the most popular ways to deal with the filtering problem is the celebrated Kalman filtering approach, which generally provides an optimal estimation of the state variables in the sense that the covariance of the estimation error is minimized [1]. This approach usually requires the exact information on both the external noises and the internal model of the system. However, these requirements are not always satisfied in practical applications. To overcome these difficulties, an alternative approach called filtering has been introduced, which aims to determine a filter such that the resulting filtering error system is asymptotically stable, and the -induced norm (for continuous systems) or -induced norm (for discrete systems) from the input disturbances to the filtering error output satisfies a prescribed performance level. In contrast to the Kalman filtering approach, the filtering approach does not require exact knowledge of the statistical properties of the external noise, which renders this approach very appropriate in many practical applications. A great number of filtering results have been reported, and various approaches, such as the linear matrix inequality (LMI) approach [2], polynomial equation approach [10], algebraic Riccati equation approach [19], [22], and frequency domain approach [21], have been proposed in the literature. When parameter uncertainties appear in a system model, the robust filtering problem has been investigated, and some results on this topic have been presented; see, e.g., [5], [8], [12], [27], and the references therein. It is worth pointing out that these results were obtained in the context of one-dimensional (1-D) systems.
