Weak Decoupled State and Mode Feedback Controller Design for Discrete-Time Markovian Jump Linear Systems

Abstract

This paper considers the design of a weak decoupled state and mode feedback controller for discrete-time Markovian jump linear systems(MJLSs). The proposed controller consists of two parts. The first part is a state feedback controller, which is used to stabilize the MJLS by utilizing the invariant part of the mode transition probabilities matrix(MTPM) and it can therefore stabilize the MJLS when transition probabilities matrix is partly changed. The second part of the controller is a mode feedback controller, which aims to reduce the stabilization cost on the basis of system stability and it is dependent on only the varying part of the MTPM. Due to the fact that state feedback control and mode feedback control are designed according to the different parts of MTPM, there is no direct relations between them and they are then called “weak decoupled” for this reason. Numerical examples are provided to show the validity of the proposed controller.