This paper presents the design of a state-feedback control strategy for spacecraft rendezvous in a circular target orbit, based on the Hill–Clohessy–Wiltshire (HCW) equations. The proposed approach employs an impulsive actuation mechanism in which thruster firings are triggered by a state-dependent switching condition. In contrast to existing hybrid or event-triggered impulsive control schemes, the proposed framework enables the co-design of the controller gain and the triggering condition through a unified Linear Matrix Inequality (LMI) formulation. Specifically, a quadratic switching function is introduced to determine both the control action and the state regions that activate the thrusters. Lyapunov-based analysis is used to derive LMI conditions that guarantee closed-loop stability while explicitly accounting for input constraints, process noise and reducing the number of actuation events. The resulting design allows the triggering surface and the feedback law to be jointly optimized offline, providing a systematic way to balance stability and actuation efficiency. The effectiveness of the proposed approach is illustrated through numerical simulations and compared with a standard Model Predictive Control (MPC) strategy, highlighting the trade-offs between control performance and propulsion usage.