Improved offline design for robust MPC for polytopic time-varying systems

This paper introduces a novel LMI-based approach for synthesizing robust controllers for polytopic time-varying systems within the Model Predictive Control (MPC) framework. Compared to existing methods in the literature addressing the same problem, the proposed approach offers the following improvements and innovations for the offline design: the use of parameter-dependent Lyapunov matrices; the design of controllers of arbitrary order; the simultaneous design of all controller matrices; and the incorporation of the scalar arising from the S-procedure, which typically requires a time-consuming linear search, into the synthesis conditions affinely, allowing it to be optimized jointly with the other variables. The synthesis procedure is formulated as an iterative algorithm where LMIs are solved at each iteration. The effectiveness of the proposed strategy is demonstrated through numerical examples, highlighting its feasibility and superior performance, particularly in achieving larger invariant regions compared to existing methods.