%X Piecewise affine (PWA) control laws offer an attractive solution to real-time control of linear, nonlinear and hybrid systems. In this paper we provide a compact exposition of the existing state-of-the-art methods for the synthesis of PWA control laws using optimization-based methods. %D 2010 %L eprints426 %K hybrid system; linear system; nonlinear system; optimization based method; piecewise affine control law; real time control; control system synthesis; optimisation; predictive control %A Alberto Bemporad %A W.P.M.H. Heemels %A Mircea Lazar %J Symposium on Circuits and Systems %R 10.1109/ISCAS.2010.5537905 %C 30th May- 2nd June , 2010 %B Symposium on Circuits and Systems %T On the synthesis of piecewise affine control laws %I IEEE