  The method to design exponentially stable adaptive observers is proposed for
linear time-invariant systems parameterized by unknown physical parameters.
Unlike existing adaptive solutions, the system state-space matrices A, B are
not restricted to be represented in the observer canonical form to implement
the observer. The original system description is used instead, and,
consequently, the original state vector is obtained. The class of systems for
which the method is applicable is identified via three assumptions related to:
(i) the boundedness of a control signal and all system trajectories, (ii) the
identifiability of the physical parameters of A and B from the numerator and
denominator polynomials of a system input/output transfer function and (iii)
the complete observability of system states. In case they are met and the
regressor is finitely exciting, the proposed adaptive observer, which is based
on the known GPEBO and DREM procedures, ensures exponential convergence of both
system parameters and states estimates to their true values. Detailed analysis
for stability and convergence has been provided along with simulation results
to validate the developed theory.
