Natural observers for a class of second order bilinear infinite dimensional systems

We consider a class of second order infinite dimensional bilinear systems with partial state observation. The objective is to design an observer for such a class of infinite dimensional systems that preserves the physical interpretation of the individual components of the second order system, namely that the derivative of the first component of the estimated state is identical to the second component of the estimated state. This gives rise to a natural observer wherein the observer is designed for the system in its natural second order setting. Such a natural observer guarantees that the derivative of the estimated position is equal to the estimated velocity component for all times. We extend the results of a natural observer for linear second order infinite dimensional systems to the case of second order infinite dimensional bilinear systems and provide, through the well-posedness of the resulting observer, the class of systems for which such an observer is applicable. Extensive simulation results of a representative example are included to support the proposed theoretical results.