We propose a new controller parameter adaptive law that guarantees the exponentialstability of the classical dynamic model of the tracking error without using its coordinates in theadaptive law and relaxes some classical assumptions and requirements of adaptive control theory(the need to know the sign/value of the control input gain, the need for an experimental choice ofthe adaptive law gain, and the requirement to the tracking error transfer function to be strictlypositive real considering the output feedback control). The applicability of the proposed law toadaptive state and output feedback control problems is shown. The advantages of developedapproach over the existing ones are demonstrated mathematically and experimentally.