How did medieval rulers restore order and centralize political power?

IIN 800 CHARLEMAGNE, the most powerful of the Carolingians, was crowned Holy Roman emperor. After his death his empire was divided among his grandsons, and their kingdoms were weakened by nobles vying for power. In addition, beginning around 800 western Europe was invaded by several different groups. Local nobles were the strongest power, and common people turned to them for protection. By the eleventh century, however, rulers in some parts of Europe had reasserted authority and were slowly building centralized states.