7.4    Sparse Structured H Filter Design

In this section, the non-fragile H filtering problem with sparse structure is studied.

7.4.1    Problem Statement

First, a sparse structure is defined. Consider system (7.1) and a full-order filter given by



where ξ(k) ∈ Rn is the filter state, zF(k) is the estimation of z(k), and the constant matrices AF, BF, and CF are filter matrices to be designed.

First, a method of finding a class of feasible sparse structures for the designed filter to meet a prescribed H performance requirement is presented as follows.





Ae0=[ A0BFC2AF ],Be0=[ B1BFD21 ],Ce0=[ C1CFΔCF ].

Let filter gain matrices AF,

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