@article{eprints472,
            year = {2003},
           title = {Min-max control of constrained uncertain discrete-time linear systems},
          number = {9},
           pages = {1600--1606},
          volume = {48},
           month = {September},
          author = {Alberto Bemporad and Francesco Borrelli and Manfred Morari},
         journal = {IEEE Transactions on Automatic Control },
       publisher = {IEEE},
        abstract = {For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.},
             url = {http://eprints.imtlucca.it/472/},
        keywords = {additive norm-bounded input disturbances; constrained uncertain discrete-time linear systems; constraints; continuous piecewise affine function; finite-horizon robust optimal control law; min-max control formulation; multiparametric linear programs; optimal control law; polyhedral parametric uncertainties; receding horizon scheme; robust optimal feedback controller; robustness; state feedback controllers; state vector; state-space matrices; constraint theory; control system synthesis; discrete time systems; linear programming; linear systems; minimax techniques; minimisation; optimal control; piecewise constant techniques; robust control; state feedback; state-space methods; uncertain systems}
}