$\mathcal {H}_{2}$ and $\mathcal {H}_\infty$ Suboptimal Distributed Filters Design for Linear Systems

Abstract

This paper investigates the <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> suboptimal distributed filtering problems for continuous time linear systems. We consider a linear system monitored by a number of filters, where each of the filters receives only part of the measured output of the system. Each filter can communicate with the other filters according to an a priori given strongly connected weighted directed graph. The aim is to design filter gains that guarantee the <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> or <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> norm of the transfer matrix from the disturbance input to the output estimation error to be smaller than an a priori given upper bound, while all local filters reconstruct the full system state asymptotically. We provide a centralized design method for obtaining such <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> suboptimal distributed filters. The proposed design method is illustrated by a simulation example.