In a deterministic system of which the inputs or outputs are detected with errors, the observer designed without considering the errors does not often give the efficient estimates of the states. Therefore it is necessary to construct the observer which guarantees the efficient estimates notwithstanding the errors.
Komiya and Furuta defined a bias free observer as the observer effective for the output biases which are governed by the known linear dynamical system with the unknown initial conditions, and designed it by geometric approach. But their method cannot be used in the case of such a more general class of detection errors than the biases as given by outputs of the unknown dynamical system.
In this paper we propose a design method of the detection error free observer (DEFO) by spectral decompostion approach when the detection errors belonging to C¹-class act at the outputs. The necessary and sufficient conditions are given to construct the DEFO for estimating the complete states. Furthermore, the sufficient conditions are presented to construct the DEFO for estimating the partial states. Finally, we show numerical examples of the proposed DEFO.