A contribution on the parallel adaptive observer

The relationship between series–parallel and parallel observers for single-input–single-output (SISO) systems is explored in this paper. The asymmetry existing between both observers as far as the case where they can be applied is put in evidence. For the unsolved case a globally stable solution is proposed for the parallel observer applied to a general nth order linear time-invariant (LTI) plant of SISO type, which is based on a filtered version of the output error. The solution guarantees that all signals remain bounded and the output error converges to zero. Furthermore, if persistently exciting conditions are satisfied, state estimation errors also converge to zero. Some simulations of a second-order system for the ideal case and in the presence of noise are included to verify the behavior of the proposed solution.