Asymptotic Properties of an Output-Feedback Suboptimal Control Scheme for Stochastic Bilinear Systems

The asymptotic properties of the filtering section in a feedback-control scheme for the stochastic regulation problem of noisy-observed linear systems with state-dependent noise, are studied in the present work. The feedback-control scheme consists in the suboptimal quadratic controller for which we proved a separation property and gave the complete set of equation in a previous paper. In this paper we focus our attention on the filtering part of the control scheme and prove that, under some (reasonable) conditions involving the system to be controlled, the set of matrix differential equations describing the evolution of the covariances of the system state, state-estimate, and error-estimate, have a limiting solution that can be used to implement the overall control scheme.