Enlarging the class of linear systems admitting adaptive observers without persistent excitation

A primary goal of adaptive observers would be to estimate the true states of a plant. Identification of unknown parameters is of secondary interest and is achieved frequently with the persistent excitation condition of some regressors. Nevertheless, two problems are linked to each other in the classical approaches to adaptive observers; as a result, we get a good state estimate once after a good parameter estimate is obtained. This paper focuses on the state estimation without parameter identification so that the state is estimated without persistent excitation condition. Besancon(2000) recently unified this direction of research and illustrated that most of adaptive observers in the literature share one common canonical form, in which unknown parameters do not affect unmeasured states. We consider another class of linear systems from the canonical form of Besancon(2000) by proposing an adaptive observer (with additional dynamics) that allows unknown parameters to affect those unmeasured states. A recursive algorithm is presented to design the proposed dynamic observer systematically. An example confirms the design step with a simulation result.