The rapid growth of resource-constrained mobile platforms, including mobile robots, wearable systems, and Internet-of-Things devices, has increased the demand for computationally efficient neural network controllers (NNCs) that can operate within strict hardware limitations. While deep neural networks (DNNs) demonstrate superior performance in control applications, their substantial computational complexity and memory requirements present significant barriers to practical deployment on edge devices. This paper introduces a comprehensive model compression methodology that leverages component-aware structured pruning to determine the optimal pruning magnitude for each pruning group, ensuring a balance between compression and stability for NNC deployment. Our approach is rigorously evaluated on Temporal Difference Model Predictive Control (TD-MPC), a state-of-the-art model-based reinforcement learning algorithm, with a systematic integration of mathematical stability guarantee properties, specifically Lyapunov criteria. The key contribution of this work lies in providing a principled framework for determining the theoretical limits of model compression while preserving controller stability. Experimental validation demonstrates that our methodology successfully reduces model complexity while maintaining requisite control performance and stability characteristics. Furthermore, our approach establishes a quantitative boundary for safe compression ratios, enabling practitioners to systematically determine the maximum permissible model reduction before violating critical stability properties, thereby facilitating the confident deployment of compressed NNCs in resource-limited environments.