Optimal control synthesis function of discrete-time system

For the problem that function fhan() is not the optimal control synthesis function of discrete-time system,but the likeness of the optimal control synthesis function of discrete-time system,the real optimal control synthesis function of discrete-time system,named function fsun(),is deduced,which can perfect the theory frame of active disturbance rejection control technique. Theory analysis and numerical value simulation show that there is no overflow in position and velocity curve when state variables reach steady states,if function fsun() is adopted in second-order discrete-time system. At the same time,the steps is fewer than that of function fhan() when state variables reach steady states.