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Robustification of the Synchronous Mode in a Hybrid Observer for a Continuous System under an Intrinsic Pulse-modulated Feedback

The paper deals with a hybrid observer for an oscillating system composed of a linear continuous chain structure controlled by an intrinsic pulse-modulated feedback. The observed plant portrays a biochemical system under pulsatile regulation, e.g., an impulsive mathematical model of endocrine regulation. The observer reconstructs the continuous states of the model from only from the continuous system output and no measurements of the discrete part of the plant, i.e., the timing of the feedback firing events, are available. The problem of enlarging the basin of attraction of a synchronous observer mode that corresponds to a zero solution of the hybrid observer error is considered. It is demonstrated that the asymmetricity of the basin of attraction in the case of a static observer gain leads to a slow observer convergence and can be effectively alleviated through the introduction of a dynamical feedback.