Disturbance Attenuation and Rejection for Discrete-Time Markovian Jump Systems

Abstract

This chapter addresses the disturbance attenuation and rejection problem for discrete-time MJLs with lossy measurements and multiple disturbances. The measurements transmitted from the plant to the observer and the controller are assumed to be imperfect, and two stochastic variables are utilized to model the missing data separately. A DOB control and $\mathcal {H}_{\infty }$ control scheme is proposed for attenuating and rejecting the disturbances. This method is focused on the design of a new structure for the disturbance observer, dynamic output feedback controller, and composite controller, such that the composite system is stochastically stable and it satisfies scheduled performance requirements. The computation-oriented conditions of the disturbance observer gains and controller matrices for the controlled plant are provided based on the piecewise quadratic Lyapunov functional approach. Finally, a numerical example is provided to demonstrate the utility and applicability of the proposed theoretical method.