Robustness margin for piecewise affine explicit control law

Abstract : — Classical robustness margin i.e., gain margin and phase margin, considers the gain variation and phase variation of the model preserving the stability of the closed loop. In this paper, an attempt to find the same kind of margin for a piecewise affine (PWA) controller is done. This controller usually obtained in explicit model predictive control (MPC) is defined over a convex region of the state space X. Starting from the invariance property of the closed loop obtained with a discrete dynamic model and PWA controller in a convex region of the state space, we calculate two robustness margin preserving this invariance property. The first one will be denoted as gain margin corresponding to the variation of the gain of the model guaranteeing the invariance. The second one, that we call, the robustness margin against first order neglected dynamics correspond to the smallest first order neglected dynamic allowed in the system preserving the invariance property.