Switched Robust Model Predictive Control With Structured Feedback Uncertainty

Abstract

This article presents a novel switched robust model predictive control (SR-MPC) framework for uncertain systems with structured feedback uncertainty. Unlike traditional approaches, this proposed framework uniquely unifies the Lyapunov-Metzler stability theorem with linear fractional representation to ensure robust stability under structured uncertainties through a switching control law formulated via linear matrix inequalities (LMIs). The method supports both online and offline implementations with either state or output feedback, offering greater flexibility compared to conventional MPC techniques. To establish feasibility and stability, three theorems provide an LMI-based test that certifies the robustness of the closed-loop controller-observer system, computes the look-up table gains, and determines the boundary invariant ellipsoids defining regions of asymptotic stability. Comparative simulations demonstrate that the proposed strategy outperforms benchmark designs in terms of time response and time-domain integral performance indices. The results highlight the enhanced stability and robustness of SR-MPC, reinforcing its significance as a contribution to MPC theory and practice.