YOu are right that the term 'sleeping partner' is not defined in the partnership act. But section 5 of the same act says that the relation among the partner arises from the contract.
Further, Section 13 of the same act defines rights and liabilities of the partners but this is subject to the contract between the partners. So the relation and the status of the partner among themselve depends on the partnership deed which is a valid contract among the partners.
So, the sleeping partner is the partner in the firm as defined in the partner ship deed and his rights and liabilities depends on terms and conditions written in the deed.