Adaptive observer of state and disturbances for linear overparameterized systems

The problem of state reconstruction is considered for a class of linear systems with time-invariant unknown parameters and overparameterization that are affected by external perturbations generated by a known exosystem with unknown initial conditions. An extended adaptive observer is proposed, which, in contrast to existing approaches, solves state and perturbation adaptive estimation problems for systems that are not represented in the observer canonical form. The obtained theoretical results are validated via mathematical modeling.