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The method to design exponentially stable adaptive observers is proposed forlinear time-invariant systems parameterized by unknown physical parameters.Unlike existing adaptive solutions, the system state-space matrices A, B arenot restricted to be represented in the observer canonical form to implementthe observer. The original system description is used instead, and,consequently, the original state vector is obtained. The class of systems forwhich the method is applicable is identified via three assumptions related to:(i) the boundedness of a control signal and all system trajectories, (ii) theidentifiability of the physical parameters of A and B from the numerator anddenominator polynomials of a system input/output transfer function and (iii)the complete observability of system states. In case they are met and theregressor is finitely exciting, the proposed adaptive observer, which is basedon the known GPEBO and DREM procedures, ensures exponential convergence of bothsystem parameters and states estimates to their true values. Detailed analysisfor stability and convergence has been provided along with simulation resultsto validate the developed theory.

Exponentially Stable Adaptive Observation for Systems Parameterized by Unknown Physical Parameters