Decentralized $H_{2}$ Control for Multi-Channel Stochastic Systems

This technical note investigates a decentralized H
₂
control problem for multi-channel linear time-invariant stochastic systems governed by Itô's differential equation. After using a stochastic algebraic Riccati equation (SARE) to establish the necessary conditions for the existence of the optimal strategy set that minimizes an H
₂
norm, we show that the necessary conditions can also be expressed using a linear matrix inequality (LMI). The equivalence between the solvability of the SARE and the feasibility of the LMI is proved for the first time using a Karush-Kuhn-Tucker (KKT) condition. Furthermore, the static output feedback solution was also studied. A numerical example is given to demonstrate the usefulness of the obtained features.