This paper addresses the simultaneous design of observer-based robust scaled-H8 controllers and scaling matrices for discrete-time linear time-invariant polytopic systems. Based on the so-called dilated linear matrix inequality approach, we propose a design method for our problem with a structural constraint for the decision matrix which is introduced in “dilation” procedure. The structural constraint inevitably introduces conservatism; however, numerical examples illustrate the effectiveness of the simultaneous design of controller matrices, i.e. observer gain, state-feedback gain, the state transition matrix of the observer, and the input or the output matrix of the observer, as well as the scaling matrix.