On the uniqueness of the simple adaptive controller gains

The existence and uniqueness of the adaptive gain matrices are examined for the simple adaptive controller (SAC). The existence and uniqueness of the ideal trajectory reference gains are derived by using the properties of the extended Lyapunov equation. The convergence of the adaptive gains to the reference gains is then examined numerically with and without the corrupting effect of the filtering gains σ and the unmeasurable excitations. These results, together with the corrupting effect of the noise and the filtering gain σ, are demonstrated by numerical examples