When talking about preferences in LQ DP it is said that for the state and the control, loss is measured as squared distance from the origin. Additionally, it is said that R and Q can identify other – non-Euclidean – notions of “distance” from the zero vector,

My question is how can I transform R and Q and the expression of losses (5) to account from Manhattan distances (L_1) or even Chebyshev distances (L_{\infty})?