Rigorous Stability Analysis of Command Generator Tracking-Beyond the Averaging Method

摘要

The adaptive law in time-varying form is transformed into the time-invariant form for the command generator tracking method by the transformation to a rotating frame. This transformation is rigorous, and the resultant adaptive law in time-invariant form gives the rigorous stability condition. For concreteness, this condition is applied to a second-order system. The rigorous stability condition is obtained and compared with that derived from the averaging method. It is shown that the rigorous stability condition gives the bonds of adaptive gain for each input frequency.