Of course, you must honor the terms of your lease as it is a legal contract. Most leases have a clause about how many days a landlord has to give to notify the tenant the lease will not be renewed. If there is no notification, most leases convert to month-to-month. Once you are month to month, you can really change it any time with 30 days notice.
Now most people will want to give the tenant a few extra days to think about things, but you are basically giving the the option to sign a new lease or move out.
One of my property managers also uses an incentive to get them to sign, rather than drag things out. He notifies the tenant that if they choose to stay month-to-month their rent will go up $100/mo but if they sign the new 12--month lease, the rent goes up only $25/mo. That can actually be beneficial for both parties. If the tenant wants to stay 2 more months and then leave, they aren't forced to leave early or lock in a 12 month commitment.