I. Necoara, B. De Schutter, W.P.M.H. Heemels, S. Weiland, M. Lazar, and T.J.J. van den Boom, "Control of PWA systems using a stable receding horizon method," Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, pp. 123-128, July 2005.
In this paper we derive stabilization conditions for the class of piecewise affine (PWA) systems using the linear matrix inequality (LMI) framework. We take into account the piecewise structure of the system and therefore the matrix inequalities that we solve are less conservative. Using the upper bound of the infinite-horizon quadratic cost as a terminal cost and constructing also a convex terminal set we show that the receding horizon control stabilizes the PWA system. We derive also an algorithm for enlarging the terminal set based on a backward procedure; therefore, the prediction horizon can be chosen shorter, removing some computations off-line.