authority

1. Institutionalized and legal power inherent in a particular job, function, orposition that is meant to enable its holder to successfully carry out his or her responsibilities. 
2. Power that is delegated formally. It includes a right to command a situation, commit resources, give orders and expect them to be obeyed, it is always accompanied by an equal responsibility for one's actions or a ...

Everyone in school respected the tough new principal's authority and no one disobeyed him, not even the older, more difficult students.