A Stabilizing Controller for Jump Linear Gaussian Systems with Noisy State Observations

Abstract

The importance of jump linear systems in modelling practical physical systems, e.g., tracking, repairable systems, systems subject to abrupt changes etc., has drawn extensive attention. Results have been obtained in control, stabilization and filtering, when the mode (system model) is assumed to be directly and perfectly observed, which, in many applications, is an unrealistic assumption. When this is not the case, there have been few methods to find a stabilizing controller when the modes are not observed and the base state is observed only in the presence of noise. A stabilizing controller was recently proposed for the case that the modes are not observed but the base state is perfectly available. In this work, we extend the result to the case that not only the modes are not observed but also the base state is partially measured through a noisy channel. We also show that the stabilizing controller possesses a desirable robustness property with respect to the mode probability transition matrix and the system dynamic model.