$H_{2}$ Performance Analysis and Distributed $H_{2}$ Control of Interconnected Large-Scale Systems

This article considers the
$H_{2}$
performance analysis and distributed
$H_{2}$
control problems of interconnected large-scale systems (LSSs). According to the developed space construction approach, both novel necessary and sufficient conditions are established to ensure the asymptotic stability and
$H_{2}$
performance of the studied LSSs. Next, these investigated results are utilized to derive some sufficient conditions for the existence of the
$H_{2}$
distributed controllers. The desired distributed controller gains are constructed via the solutions of some developed linear matrix inequality conditions, which guarantee the stability and the
$H_{2}$
performance of the closed-loop LSSs. Finally, three examples are introduced to show the superiority and validity of the proposed theoretical method.