Stability analysis of piecewise affine systems with multi-model predictive control

Abstract

We propose an input–output stability analysis for closed-loop systems of piece-wise affine models under unstructured uncertainty and controlled by multi-model linear MPC with input constraints. Integral quadratic constraints (IQCs) are employed to assess the robustness of MPC under uncertainty. We efficiently create a model pool, by performing linearization on selected transient points. All the possible uncertainties and nonlinearities (including the controller) can be introduced in the framework, assuming that they admit the appropriate IQCs, whilst the dissipation inequality can provide sufficient conditions for stability through the incorporation of IQCs. We demonstrate the existence of static multipliers, which can reduce the conservatism of the stability analysis significantly. The proposed methodology is demonstrated through two illustrative case studies.