A. Airan, M. Bhushan, and S. Bhartiya, Linear Machine Solution to Point Location Problem, IEEE Transactions on Automatic Control, vol.62, issue.3, 2016.
DOI : 10.1109/TAC.2016.2573201

G. Aloupis, H. Pérez-rosés, G. Pineda-villavicencio, P. Taslakian, and D. Trinchet-almaguer, Fitting Voronoi Diagrams to Planar Tesselations, Combinatorial Algorithms, pp.349-361, 2013.
DOI : 10.1007/978-3-642-45278-9_30

URL : http://arxiv.org/pdf/1308.5550.pdf

F. Aurenhammer, A criterion for the affine equivalence of cell complexes inR d and convex polyhedra inR d+1, Discrete & Computational Geometry, vol.49, issue.1, pp.49-64, 1987.
DOI : 10.2307/1969055

D. Avis and K. Fukuda, A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra, Discrete & Computational Geometry, vol.8, issue.3, pp.295-313, 1992.
DOI : 10.1016/0095-8956(85)90042-5

M. Baotic, F. Borrelli, A. Bemporad, and M. Morari, Efficient On-Line Computation of Constrained Optimal Control, SIAM Journal on Control and Optimization, vol.47, issue.5, pp.2470-2489, 2008.
DOI : 10.1137/060659314

F. Bayat, T. A. Johansen, and A. A. Jalali, Using hash tables to manage the time-storage complexity in a point location problem: Application to explicit model predictive control, Automatica, vol.47, issue.3, pp.571-577, 2011.
DOI : 10.1016/j.automatica.2011.01.009

A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, The explicit linear quadratic regulator for constrained systems, Automatica, vol.38, issue.1, pp.3-20, 2002.
DOI : 10.1016/S0005-1098(01)00174-1

F. Borrelli, M. Baoti´cbaoti´c, J. Pekar, and G. Stewart, On the computation of linear model predictive control laws, Automatica, vol.46, issue.6, pp.1035-1041, 2010.
DOI : 10.1016/j.automatica.2010.02.031

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

H. Crapo and W. Whiteley, Plane self stresses and projected polyhedra 1: the basic pattern, Structural Topology, vol.19, pp.55-73, 1993.

H. Edelsbrunner and R. Seidel, Voronoi diagrams and arrangements, Discrete & Computational Geometry, vol.24, issue.1, pp.25-44, 1986.
DOI : 10.1093/comjnl/24.2.167

URL : http://ecommons.cornell.edu/bitstream/1813/6509/1/85-669.pdf

T. Gal, Postoptimal analyses, parametric programming and related topics, 1995.
DOI : 10.1515/9783110871203

A. Grancharova and T. A. Johansen, Explicit Nonlinear Model Predictive Control, 2012.
DOI : 10.1007/978-3-642-28780-0

B. Grünbaum, Convex polytopes, 1967.

M. Gulan, N. A. Nguyen, S. Olaru, P. Rodriguez-ayerbe, and B. Rohal-'-ilkiv, Implications of Inverse Parametric Optimization in Model Predictive Control, Developments in Model-Based Optimization and Control, pp.49-70, 2015.
DOI : 10.1016/S0005-1098(02)00250-9

URL : https://hal.archives-ouvertes.fr/hal-01259959

M. Gulan, G. Takács, N. A. Nguyen, S. Olaru, P. Rodriguez-ayerbe et al., Embedded linear model predictive control for 8-bit microcontrollers via convex lifting, the 20th IFAC World Congress, 2017.
DOI : 10.1016/j.ifacol.2017.08.2220

D. Hartvigsen, Recognizing Voronoi Diagrams with Linear Programming, ORSA Journal on Computing, vol.4, issue.4, pp.369-374, 1992.
DOI : 10.1287/ijoc.4.4.369

M. Herceg, M. Kvasnica, C. Jones, and M. Morari, Multi-Parametric Toolbox 3.0, European Control Conference (ECC), pp.502-510, 2013.

K. H. Johansson, The quadruple-tank process: a multivariable laboratory process with an adjustable zero, IEEE Transactions on Control Systems Technology, vol.8, issue.3, pp.456-465, 2000.
DOI : 10.1109/87.845876

M. Kvasnica and M. Fikar, Clipping-Based Complexity Reduction in Explicit MPC, IEEE Transactions on Automatic Control, vol.57, issue.7, pp.1878-1883, 2012.
DOI : 10.1109/TAC.2011.2179428

M. Kvasnica, J. Hledík, I. Rauová, and M. Fikar, Complexity reduction of explicit model predictive control via separation, Automatica, vol.49, issue.6, pp.1776-1781, 2013.
DOI : 10.1016/j.automatica.2013.02.018

M. Kvasnica, B. Takács, J. Holaza, and S. D. Cairano, On region-free explicit model predictive control, 2015 54th IEEE Conference on Decision and Control (CDC), pp.3669-3674, 2015.
DOI : 10.1109/CDC.2015.7402788

J. C. Maxwell, On reciprocal diagrams and diagrams of forces, Philosophical Magazine, vol.4, issue.27, pp.250-261

N. A. Nguyen, Explicit robust constrained control for linear systems: analysis, implementation and design based on optimization, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01261034

N. A. Nguyen, S. Olaru, P. Rodriguez-ayerbe, M. Hovd, and I. Necoara, Fully Inverse Parametric Linear/Quadratic Programming Problems via Convex Liftings, Developments in Model-Based Optimization and Control, pp.27-47
DOI : 10.1016/S0005-1098(02)00250-9

URL : https://hal.archives-ouvertes.fr/hal-01259951

N. A. Nguyen, S. Olaru, and P. Rodriguez-ayerbe, Any discontinuous PWA function is optimal solution to a parametric linear programming problem, 2015 54th IEEE Conference on Decision and Control (CDC)
DOI : 10.1109/CDC.2015.7403151

URL : https://hal.archives-ouvertes.fr/hal-01259879

N. A. Nguyen, S. Olaru, P. Rodriguez-ayerbe, M. Hovd, and I. Necoara, On the lifting problems and their connections with piecewise affine control law design, 2014 European Control Conference (ECC), pp.2164-2169, 2014.
DOI : 10.1109/ECC.2014.6862605

URL : https://hal.archives-ouvertes.fr/hal-01087243

R. Oberdieck and E. N. Pistikopoulos, Explicit hybrid model-predictive control: The exact solution, Automatica, vol.58, pp.152-159
DOI : 10.1016/j.automatica.2015.05.021

S. Olaru and D. Dumur, A parameterized polyhedra approach for explicit constrained predictive control, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), pp.1580-1585, 2004.
DOI : 10.1109/CDC.2004.1430269

K. Rybnikov, Polyhedral partitions and stresses, 1999.

A. Schrijver, Theory of linear and integer programming, 1998.

A. Schulz, M. M. Seron, G. C. Goodwin, and J. A. Doná, Lifting planar graphs to realize integral 3-polytopes and topics in pseudo-triangulations Characterisation of receding horizon control for constrained linear systems, Ph.D. dissertation, Fachbereich Mathematik und Informatik der Freien, pp.271-286, 2003.

P. Tøndel, T. A. Johansen, and A. Bemporad, Evaluation of piecewise affine control via binary search tree, Automatica, vol.39, issue.5, pp.945-950, 2003.
DOI : 10.1016/S0005-1098(02)00308-4