Necessary and sufficient condition of distributed H∞ filtering for interconnected large-scale systems: A novel space construction approach

This paper studies the distributed $H_{\infty }$ filtering problem for interconnected large-scale systems (ILSs). In distributed filtering, all sub-filters are interconnected via the designed interconnection matrix and each filter only requires local subsystems’ measurements to estimate the target signals. By the developed space construction method, novel both necessary and sufficient conditions are proposed to ensure the asymptotic stability and $H_{\infty }$ performance of the filtering error ILSs. The novel conditions are numerically attractive because the computationally expensive matrix inversion terms are eliminated. In order to further reduce the computation burden, some sufficient conditions are also provided to guarantee the stability and $H_{\infty }$ performance of the filtering error for ILSs. Then, by constructing the basis of the null space for some matrices skillfully and using Finsler’s Lemma three times, this paper separates the product relation among the filter parameters and the unknown auxiliary variables. As a result, not only the filter parameters but also the interconnection matrix of distributed filters can be designed. The designed conditions are given in terms of linear matrix inequalities. At last, three examples are tested to demonstrate the advantages and superiorities of the developed filtering methodology.