Conditional Stability of a State Observer for a Low-order Hybrid Plant

Dynamical behaviors in a recently proposed observer for linear time-invariant systems with intrinsic pulse-modulated feedback are studied. A special case of scalar linear dynamics is considered as it is not covered by the previously presented mathematical analysis. Notably, the lowest non-trivial dimension of the continuous part of the plant results in 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 dimension continuous dynamics.