Exponentially Stable Adaptive Observation for Systems Parameterized by Unknown Physical Parameters

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 four assumptions related to: first, the boundedness of a control signal and all system trajectories, second, the identifiability of the physical parameters of
A
and
B
from the numerator and denominator polynomials of a system input/output transfer function, third, the complete observability of system states, and four, the parametrizability of a linear regression equations with respect to system matrices and Luenberger correction gain. 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.