The discrete time-variant regulator problem with an infinite sum criterion is considered as a variational problem on the normed linear apace of infinite sequences(1n1)The discrete Euler equation is used to find the necessary condition that an optimal control sequence, solving this problem, must satisfy and it is shown that the optimal control is in the form of time-variant feedback gain which satisfies a discrete Riccati difference equation. The case of finite-time, time-variant regulator is treated as a special case of the infinite-time problem.