State observer for a low-order plant under intrinsic pulse-modulated feedback: A case study

Dynamical behaviors in a recently proposed observer for linear time-invariant systems under intrinsic pulse-modulated feedback are studied. A special case of scalar continuous dynamics is considered as it is not covered by the previously presented mathematical analysis. Notably, the lowest non-trivial differential order of the continuous part of the plant results in a more complex dynamics of the observer. In fact, the convergence of the observer becomes dependent on the observer initialization, which phenomenon does not exist in the case of the second and higher order continuous dynamics. As an alternative to the static gain observer, an integral feedback observer is suggested that exhibits global convergence for certain values of the observer gain and types of the periodic solution in the observed plant. Extensive bifurcation analysis is though necessary to select a proper observer gain.