Superiority of LiT discrete/continuous control compared to ZOH control in the DT LQR problem

Recently, a generalization of the conventional (ZOH) discrete time control method called “discrete continuous (D/C) control”, was introduced in the control literature. In that generalization the discrete time control is allowed to vary continuously with time in an open loop fashion, across each sampling interval t_k<t<t _k+1. The discrete continuous control method was applied to the discrete time linear quadratic regulator (LQR) problem in a 1996 SSST paper. A detailed analytical analysis of the closed loop performance of a special case of D/C LQR control, called “linear in time” (LIT), is developed to obtain necessary and sufficient conditions for its superiority in comparison to the closed loop performance of the conventional ZOH LQR control. Some examples are presented to illustrate the analytical results