Decentralized H2 control for multi-channel stochastic systems via state feedback strategies: Application to multimodeling systems

This paper investigates a decentralized H₂ state feedback control for multi-channel linear time-invariant stochastic systems governed by Itoô´s differential equation. After establishing the necessary condition based on stochastic algebraic Riccati equation (SARE) for the existence of the strategy set, it is shown that the same conditions can be written by the linear matrix inequality (LMI). The equivalence between the solvability of the SARE and the feasibility of the LMI is proved for the first time by using the Karush-Kuhn-Tucker (KKT) condition. In order to prove the usefulness of the proposed methodology, the extension to the multiparameter singularly perturbed systems (MSPS) is also considered. It is shown that the parameter-independent strategy set can be designed by solving the reduced-order AREs and LMI. Furthermore, as a novel contribution, the degradation of H₂ norm for the closed-loop stochastic systems by means of the parameter independent strategy set that is yielded via LMI methods is given. A numerical example is given to demonstrate the useful feature obtained.