Trajectory tracking problem for Markov jump systems with Itô stochastic disturbance and its application in orbit manoeuvring

This paper deals with the trajectory tracking problem for jump systems with Itô stochastic disturbance. The main contribution is that the form of the controller is complete parametric. The controller consists of the additive contribution of two terms: a feedback term and a feedforward term. The feedback term is presented using the linear matrix inequality method for the state feedback control law to make the system stochastically stable and can guarantee the input constraints. The feedforward term is the complete parametric feedforward tracking compensator by utilizing the parametric solution of the generalized Sylvester matrix equation for the trajectory tracking problem. The simulation about spacecrafts hovering task is carried out in relative orbit manoeuvring control. The simulation results show the effectiveness of the proposed approach.