Your task is to create a simple personnel management system using Python. The system should be capable of handling a Person class. A Person is characterized by a name and age.
A Person can introduce themselves by stating: "My name is <name> and I am <age> years old.".
However, the system should be able to validate the ages of the people. If the age is not a positive integer or if the age is more than 130 (since that's more than the verified oldest person ever), an AgeError should be thrown.