The previous chapter studied the non-fragile controller design problem with the additive interval-bounded coefficient variations consideration. Similar to the control problem, the analysis and design problems of H filtering have been investigated extensively over the last two decades and many approaches have been developed [see, for example, 29, 38, 41, 138, and references therein]. An implicit assumption in the above mentioned works is that the filter will be implemented exactly. However, similar to the controller implementation, in the course of filter implementation based on different design algorithms, it also turns out that the filters can be sensitive with respect to errors in the filter coefficients [27, 147]. Also, due to the requirement of computational efficiency in real-time applications, it is highly desirable for a filter to have a sparse structure, which contains many trivial parameters.