arXiv:2611.05910v1 Announce Type: new Abstract: Optimizing digital control for power converters typically involves designing continuous-time controllers and discretizing them via Euler, Tustin, or Generalized Bilinear Transform (GBT) methods. However, the intrinsic coupling between continuous-domain control parameters and discrete-domain implementation parameters remains underexplored, often leading to suboptimal performance. To bridge this gap, this paper first establishes a Non-Uniqueness Theorem, elucidating the coupling mechanism between dual-domain parameters. Based on this, two co-design methodologies are proposed to derive optimized parameter sets: the Explicit Frequency-Domain Analytical Method (EFDAM) and the Implicit Computer-Aided Search Method (ICASM). The EFDAM derives closed-form solutions by maximizing the crossover frequency and resonant magnitude via logarithmic frequency stability criteria, while minimizing discretization errors using Taylor-series bounds. The ICASM formulates the search for optimized parameters as a constrained multi-objective optimization problem, balancing bandwidth, resonant magnitude, and fundamental magnitude. To solve ICASM efficiently, two algorithms are introduced: the Multi-Start COBYLA (MS-COBYLA), which employs Latin Hypercube Sampling for physics-informed initialization to escape local optima, and the PSO-COBYLA hybrid algorithm, which couples global particle swarm exploration with local refinement. Experimental results on a 5-kW single-phase inverter with a Proportional-Integral-Resonant (PIR) regulator validate that the proposed methods outperform the conventional benchmark, achieving a 43.3\% reduction in the peak-to-peak current ripple measured at the zero-active-power operating point and an 11.7\%--35.9\% decrease in THDi across various harmonic profiles.