  The problem of state reconstruction is considered for uncertain linear
time-invariant systems with overparameterization, arbitrary state-space
matrices and unknown additive perturbation described by an exosystem. A novel
adaptive observer is proposed to solve it, which, unlike known solutions,
simultaneously: (i) reconstructs the physical state of the original system
rather than the virtual state of its observer canonical form, (ii) ensures
exponential convergence of the reconstruction error to zero when the condition
of finite excitation is satisfied, (iii) is applicable to systems, in which
mentioned perturbation is generated by an exosystem with fully uncertain
constant parameters. The proposed solution uses a recently published
parametrization of uncertain linear systems with unknown additive
perturbations, the dynamic regressor extension and mixing procedure, as well as
a method of physical states reconstruction developed by the authors. Detailed
analysis for stability and convergence has been provided along with simulation
results to validate the theoretical analysis.
