Dynamic Output Feedback MPC of Polytopic Uncertain Systems: Efficient LMI Conditions

We focus on the design of an efficient dynamic output feedback model predictive control (DOFMPC) for linear systems with both polytopic and additive uncertainties. We tackle the problem of bilinear matrix inequality formulation which is often encountered in this type of work. In order to formulate a numerically traceable optimization problem, expressed in terms of linear matrix inequalities (LMIs), we propose a new convex stability condition by the utilization of a relaxation formula. Moreover, other inequality conditions in the optimization problem are tailored so that an efficient LMI optimization problem is formulated. Unlike in previous works, the proposed approach does not require any special structure of system matrices, which results in more flexibility. The effectiveness of the proposed approach is verified through a numerical example.