| Abstract: | We study the stability of the equilibria of the differential equations that describe an adaptive controller in closed loop with a linear time-invariant (LTI) undermodelled plant when the parameter update law is a leaky gradient, i.e. a s?-modified estimator. Hsu and Costa studied the full-order case and showed that under certain limiting conditions the resulting dynamic system has three, possibly unstable, equilibrium points. Here we provide a modest extension to that work by further characterizing the class of undermodelled LTI plants for which the equilibria exist and are (un)stable Interestingly enough, it is shown that the equilibria are stable iff a given compensator stabilizes the plant. This compensator is, up to the plant ‘steady state gain’, known to the designer. |
