Stabilization of Discrete-Time Multiplicative-Noise System Under Decentralized Controllers

In this article, we study the mean-square stabilization of discrete-time multiplicative-noise stochastic systems under decentralized controllers. Two controllers are involved in the system where each controller has access to different information and one information set is contained by another one. The adopted information structure is adapted open-loop. The main contribution of the article is twofold. On one hand, we give the unique explicit solution of the finite-horizon optimization problem in terms of difference Riccati equations. On the other hand, we characterize the equivalent condition for the mean-square stabilization under the decentralized controllers via the corresponding algebraic Riccati equations. Moreover, we derive the optimal and stabilizing solution for the infinite-horizon optimization problem.