  We consider a class of uncertain linear time-invariant overparametrized
systems affected by bounded disturbances, which are described by a known
exosystem with unknown initial conditions. For such systems an exponentially
stable extended adaptive observer is proposed, which, unlike existing
solutions, simultaneously: (i) allows one to reconstruct original (physical)
states of the system represented in arbitrarily chosen state-space form rather
than virtual states of the observer canonical form; (ii) ensures convergence of
the state observation error to zero under weak requirement of the regressor
finite excitation; (iii) does not include Luenberger correction gain and forms
states estimate using algebraic rather than differential equation; (iv)
additionally reconstructs the unmeasured external disturbance. The proposed
solution is based on the new parametrizations to identify the observer
parameters obtained with the help of the heterogeneous mappings and the dynamic
regressor extension and mixing procedure. Illustrative simulations support
obtained theoretical results.
