Design and input-to-state practically stable analysis of the mixed H2/H∞ feedback robust model predictive control

In this study, the authors address the problem of the mixed H₂/H_∞ robust model predictive control (RMPC) for a class of discrete-time systems with structured uncertainty and disturbances. The conditions of RMPC are given to satisfy both the H₂ and H_∞ performance requirements. In order to reduce the conservativeness caused by an unique feedback control law, a multi-step control strategy is introduced to improve the control performance and enlarge the feasible region of RMPC. Furthermore, an efficient version of the proposed RMPC is also given to reduce the online computational burden, which makes the design more practical. The proposed RMPCs are proven to be input-to-state practically stable (ISpS). A numerical example illustrates the effectiveness of the proposed designs.