Continuous-time design of discrete-time control systems

Two approaches to the synthesis of a discrete-time controller for a continuous-time system are presented and compared. The first one. purely discrete, bases on the discrete-time model of a dynamic system and on a discrete quadratic infinite horizon performance index while the second is based on the continuous-time integral performance index. When the sampling time tends to zero the first solution does not converge to its continuous time prototype whereas the second one does.