Exponentially stable adaptive control. Part I. Time-invariant plants

We propose a new controller parameter adaptive law that guarantees the exponential stability of the classical dynamic model of the tracking error without using its coordinates in the adaptive 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 of the adaptive law gain, and the requirement to the tracking error transfer function to be strictly positive real considering the output feedback control). The applicability of the proposed law to adaptive state and output feedback control problems is shown. The advantages of developed approach over the existing ones are demonstrated mathematically and experimentally.