Distributed Stabilization of Two Interdependent Markov Jump Linear Systems with Partial Information

TL;DR

This paper addresses the stabilization of two interdependent Markov jump linear systems with partial mode information, proposing centralized and distributed controllers and deriving conditions for stochastic stabilization.

Contribution

It introduces a framework for interdependent MJLSs with partial information and designs controllers for stabilization under different information structures.

Findings

Distributed controllers successfully stabilize the system.

Derived sufficient conditions for stabilization.

Numerical example demonstrates controller effectiveness.

Abstract

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.