A computer-implemented method for the design and implementation of optimal multivariable MPC controllers for fast-sampling constrained dynamic systems, said computer-method comprising: providing a state observer for determining a plurality of values associated with a constrained dynamic system in order to generate a plurality of state variables thereof; and implementing an explicit quadratic programming solver having an off-line part and an on-line part, said explicit quadratic programming solver adapted to solve at least one explicit quadratic programming problem utilizing an optimization algorithm being a primal-dual feasibility algorithm, wherein said explicit quadratic programming solver computes a plurality of control signals based on said plurality of state variables and a plurality of matrices stored in said off-line part of said explicit quadratic programming solver in order to provide an optimal MPC multivariable controller applicable to said constrained dynamic system, wherein, to determine primal-dual feasibility: in the off-line part, using said optimization algorithm to compute and store matrices defining constraints of said quadratic programming problem and to calculate vectors of Lagrange multipliers and an optimizer, the off-line part being run only once when user designs an MPC controller, the optimizer being an optimizer for a given parameter vector; and in the on-line part, using said optimization algorithm, by using the Lagrange multipliers and said optimizer computed in the off-line part to provide a unique optimal solution to said constrained dynamic system. providing a state observer for determining a plurality of values associated with a constrained dynamic system in order to generate a plurality of state variables thereof; and implementing an explicit quadratic programming solver having an off-line part and an on-line part, said explicit quadratic programming solver adapted to solve at least one explicit quadratic programming problem utilizing an optimization algorithm being a primal-dual feasibility algorithm, wherein said explicit quadratic programming solver computes a plurality of control signals based on said plurality of state variables and a plurality of matrices stored in said off-line part of said explicit quadratic programming solver in order to provide an optimal MPC multivariable controller applicable to said constrained dynamic system, wherein, to determine primal-dual feasibility: in the off-line part, using said optimization algorithm to compute and store matrices defining constraints of said quadratic programming problem and to calculate vectors of Lagrange multipliers and an optimizer, the off-line part being run only once when user designs an MPC controller, the optimizer being an optimizer for a given parameter vector; and in the on-line part, using said optimization algorithm, by using the Lagrange multipliers and said optimizer computed in the off-line part to provide a unique optimal solution to said constrained dynamic system. in the off-line part, using said optimization algorithm to compute and store matrices defining constraints of said quadratic programming problem and to calculate vectors of Lagrange multipliers and an optimizer, the off-line part being run only once when user designs an MPC controller, the optimizer being an optimizer for a given parameter vector; and in the on-line part, using said optimization algorithm, by using the Lagrange multipliers and said optimizer computed in the off-line part to provide a unique optimal solution to said constrained dynamic system.