This paper develops a suboptimal safety-critical control framework for nonlinear systems subject to time-varying constraints by integrating barrier-state augmentation with the state-dependent Riccati equation (SDRE) technique. First, a single-barrier design guarantees asymptotic stabilization and forward invariance of slowly evolving safe sets.Next, a multibarrier extension assigns each safety constraint its own barrier state and weighting factor, enabling independent tuning of conservativeness. At each time step, the controller solves a pointwise SDRE for the augmented dynamics. We establish that, provided the employed state-dependent coefficient (SDC) representation is pointwise controllable and observable, the origin of the closed-loop system remains asymptotically stable as long as the variation rates of the safety constraints are bounded. A key extension addresses scenarios where safety constraints and stabilization objectives are in conflict, ensuring forward invariance of time-varying safe sets even when the origin may belong to the unsafe set. To this end, we introduce a conflict-resolution barrier state and a discounted cost formulation that prioritizes safety over stability until constraints realign. Simulation results on mobile-robot collision avoidance and quadrotor navigation tasks show strict enforcement of time-varying constraints, successful handling of conflicts, and up to 50% faster computation than standard CBF-QP methods, demonstrating the real-time viability of the proposed method for complex safety-critical applications.
