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The problem of state reconstruction is considered for uncertain lineartime-invariant systems with overparametrization, arbitrary state-space matricesand unknown additive perturbation described by an exosystem. A novel adaptiveobserver is proposed to solve it, which, unlike known solutions,simultaneously: (i) reconstructs the physical state of the original systemrather than the virtual state of its observer canonical form, (ii) ensuresexponential convergence of the reconstruction error to zero when the conditionof finite excitation is satisfied, (iii) is applicable to systems, in whichmentioned perturbation is generated by an exosystem with fully uncertainconstant parameters. The proposed solution uses a recently publishedparametrization of uncertain linear systems with unknown additiveperturbations, the dynamic regressor extension and mixing procedure, as well asa method of physical states reconstruction developed by the authors. Detailedanalysis for stability and convergence has been provided along with simulationresults to validate the results of the theoretical analysis.

Parameter Estimation-Based States Reconstruction of Uncertain Linear Systems with Overparameterization and Unknown Additive Perturbations