Robust stability analysis for barrier-based equation-free multi-linear model predictive control

•We have developed a stability analysis framework for barrier based multi-model MPC.•The analysis is conducted for equation-free reduced order systems.•The analysis accounts the model error produced by the model reduction.•Two integral quadratic constraints are developed for the case of barrier-based MPC. On-line optimization strategies such as model predictive control (MPC) have been widely used to compute control actions for a range of complex industrial systems. Barrier based MPC has recently been introduced, bringing together theory and algorithms for analysing the stability of linear models, however such models may not describe complex systems dynamics adequately. Multi-model linear MPC configurations can be used as a more reliable solution as piecewise affine (PWA) models can describe the underlying nonlinear dynamics more accurately. Additionally, model order reduction can be applied to large-scale distributed systems, to reduce their dimensionality, jeopardising however their closed-loop stability. As a result, there is a clear need for an input to output stability analysis for closed loop systems under unstructured uncertainty when multi-model barrier MPC is utilized. In this work, we combine equation-free model reduction with integral quadratic constraints (IQCs) for the stability analysis of large-scale closed-loop systems under unstructured uncertainties, including model approximation errors and nonlinearities, including MPC. An illustrative example is used to elucidate the proposed methodology.