This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis results, it uses linear programming tools to address static output feedback synthesis problems with a focus on optimal gain performances. Owing to their low computational complexity, the established controller design algorithms are applicable for large-scale systems. The theory and control strategies developed will not only be useful in handling large-scale positive delay systems with improved solvability and at lower cost, but also further our understanding of the system characteristics in other related areas, such as distributed coordination of networked multi-agent systems, formation control of multiple robots.