Quadratic optimization problem for 2-D linear continuous-discrete control systems (Q1302663)

Linear 2-D continuous-discrete control systems described by differential-difference equations with constant coefficients are considered. Using algebraic methods, existence and uniqueness of the solution in a suitably defined function space are discussed. Next, the quadratic optimization problem is formally stated and solved using adjoint control systems and functional analytic methods, in particular those taken from the theory of infinite-dimensional Hilbert spaces. Moreover, several remarks and comments on continuous-discrete control systems are presented. The relations to results existing in the literature are also pointed out. Finally, it should be stressed, that similar considerations concerning optimal control of 2-D continuous-discrete control systems can be found in the paper [\textit{J. Klamka}, ``Controllability and minimum energy control of 2-D linear systems'', Proceedings of the American Control Conference, Albuquerque, June 4-6, 1997, 3141-3143 (1997)].