\begin{document}$ H_{\infty} $\end{document} observer-based control for large-scale systems with sparse observer communication network

This paper studies the \begin{document}$ H_{\infty} $\end{document} control problem for large-scale systems under a sparse observer communication network. Different from existing approaches, where the topology of the observer communication network is fixed, we aim to design the sparse observer communication network such that the closed-loop system is asymptotically stable and satisfies the \begin{document}$ H_{\infty} $\end{document} performance. Firstly, sufficient conditions are established to design the distributed \begin{document}$ H_{\infty} $\end{document} observer and controller gains in terms of LMIs. Then, the developed sufficient conditions are used to minimize the number of the links in the observer communication network. Two numerical algorithms are proposed to solve the sparse observer communication network design problem. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.