Stability analysis of an output feedback controller for the Penn State electrical ventricular assist device

The development of a controller which minimizes the energy consumption of the implanted electric ventricular assist device (EVAD) and remains stable for the duration of the implantation is considered. The EVAD model has four state variables, only one of which is measurable in vivo. An output feedback control law that utilizes the single available state and minimizes the EVAD´s energy consumption has been derived. The inclusion of the output feedback gain in the model results in a time-varying plant for which stability has to be proved. The EVAD is a pulsatile device which operates in a periodic manner. By recognizing this periodic nature, the time-varying model can be transformed into a linear time-invariant model that describes the periodic values of the system states. This linear time-variant model is used for determining whether the output feedback control law can meet the necessary and sufficient conditions for asymptotic stability