We investigate the multi-stage stochastic constrained control problem with linear dynamics and quadratic costs when only partial information of the disturbance distribution (i.e., the first two moments) is known. By constructing a distribution family or ambiguity set based on the known information, we adopt a distributionally robust chance constraint (DRCC) based approach, where the DRCC holds (with high probability) as long as the true distribution of the uncertainty belongs to the ambiguity set. We approximate the DRCC with the worst-case conditional value-at-risk (CVaR) constraint, which bounds the expected constraint violation with respect to all distributions in the ambiguity set. Although the worst-case CVaR problem is not guaranteed to be tractable in general, it is computationally tractable under linear decision rules (LDRs). To improve the performance of LDRs, we propose to apply the segregated linear decision rules (SLDRs) on dynamical control systems with the worst-case CVaR approximation. Without loss of optimality, we construct a special group of segregation leading to problems that are shown to be equivalent to tractable semidefinite programs (SDPs).