In this paper we consider a problem of sliding mode control design for LTI systems with multiplicative disturbances of the input and noisy measurements of the output. First, we apply the minimax observer to provide the best possible estimate of the system's state. Then we solve a problem of optimal reaching for the observer: we design sub-optimal control algorithms generating continuous and discontinuous feedback controls that steer the observer as close as possible to a given sliding hyperplane in a finite time. The theoretical results are illustrated by an academic example.