Distributive on-chip voltage regulation is appealing to solving the power integrity problems in nowadays high-end SoCs. Nevertheless, ensuring the stability of large-scale power delivery networks regulated by a multiplicity of voltage regulators is challenging due to the size of the system and complex interactions between the regulators and the large loading network. We present a theoretically elegant framework that provides a rigorous guarantee for network stability. We further develop a practical design approach that largely decouples the design of linear voltage regulators from that of the complex load, making it feasible to ensure the stability of the complete network. The presented design approach has been successfully applied to several design examples with guaranteed stability and competitive performances.