Model predictive control for linear parameter varying systems: a double-sum-free parameter-dependent lyapunov function approach

Abstract

We present a novel model predictive control framework for linear parameter varying (LPV) systems, leveraging a parameter-dependent Lyapunov function (PDLF) while eliminating the conventional double-sum formulation. Traditional PDLF-based approaches for LPV systems often rely on non-convex double summations, requiring approximation techniques such as sum-of-squares programming to derive tractable linear matrix inequality (LMI) conditions. These approximations introduce increased computational complexity and conservatism, limiting their practical applicability. In this paper, we show that for a class of LPV systems with a constant input matrix, it is possible to derive direct LMI conditions without any approximations by appropriately formulating the PDLF. This approach improves closed-loop performance while ensuring both recursive feasibility and asymptotic stability. Numerical comparisons with earlier solutions from the literature are given to illustrate effectiveness of the proposed method.