  In this paper, we study the stabilization of two interdependent Markov jump
linear systems (MJLSs) with partial information, where the interdependency
arises as the transition of the mode of one system depends on the states of the
other system. First, we formulate a framework for the two interdependent MJLSs
to capture the interactions between various entities in the system, where the
modes of the system cannot be observed directly. Instead, a signal which
contains information of the modes can be obtained. Then, depending on the scope
of the available system state information (global or local), we design
centralized and distributed controllers, respectively, that can stochastically
stabilize the overall interdependent MJLS. In addition, the sufficient
stabilization conditions for the system under both types of information
structure are derived. Finally, we provide a numerical example to illustrate
the effectiveness of the designed controllers.
