This chapter addresses the challenge of space power stations (SPS) attitude control under multi-source uncertainties that are both bounded and correlated. Instead of relying on traditional probabilistic methods, which require extensive sampling, a non-probabilistic framework based on convex set theory is established to quantify these uncertainties. The chapter first constructs the uncertain attitude dynamics using an extended-order state-space formulation, explicitly capturing the correlation effects among system parameters. A novel convex set-based linear quadratic regulator (CSLQR) is then developed. By deriving and solving a convex set-based algebraic Riccati equation (CSARE) alongside the Lyapunov equation, the proposed method analytically determines the bounds of feedback gains and control costs. To further ensure operational safety, a convex set-based time-dependent reliability (CSTDR) index is introduced as a dynamic assessment metric. This reliability index is subsequently integrated as a key constraint within an optimization framework to balance control performance against system safety. Numerical simulations verify that this approach effectively mitigates the impact of nonlinear dynamics and uncertainties, offering a computationally efficient alternative to Monte Carlo simulations (MCSs).