Stabilization of 2D Markov Jump Systems With Directional Communication Delays: Handling Delayed Modes and Asynchronous Modes

Abstract

This paper studies the stabilization problem of two-dimensional (2D) Markov jump systems (MJSs) with directional communication delays, where delays exist in both states and modes. Based on whether the delay mode can be directly observed, the mode-delayed and asynchronous controllers are designed, respectively. For the mode-delayed case, the closed-loop system with current modes and delayed modes is re-planned as a closed-loop 2D MJS. For the asynchronous case, an extended hidden Markov model is developed to describe the asynchronous modes in controllers. Based on the Lyapunov theory, sufficient conditions are derived to ensure the asymptotic mean square stability of the closed-loop 2D MJSs under these two cases. Finally, two different examples from a representative model of some thermal processes are verified in simulations to demonstrate the effectiveness of the designed approaches. Note to Practitioners—2D systems have found extensive applications in thermal processes, gas absorption, and water stream heating, etc. In these applications, sudden changes in parameters and structures are difficult to avoid, which will result in the system being unable to be described. Fortunately, this problem can be handled by the Markov model, which consists of modes and states. In the control problem of 2D MJSs, delayed states are usually considered in the plant. Consider a more practical case that delays exist in directional communication channels between the plant and the controller, resulting in directional delayed modes and states in the controller. In this case, how to handle these complex modes and state information and stabilize the system is of practical significance. Based on whether the delay mode can be directly observed, the mode-delayed and asynchronous controllers are designed, respectively. Finally, two different examples from a representative model of some thermal processes are verified in simulations to demonstrate the effectiveness of the designed approaches.