Exponential Stability and Input-to-State Stability of Polynomial Systems via an Observer with Sporadic Measurements

In this article, we address the problem of estimating the state of a class of polynomial systems with sporadically available measurements and external disturbance. To begin with, an observer with sporadically available measurements is designed to estimate the states of the polynomial system. We introduce a timer variable to initiate the arrival of new measurements and examine the whole system in a hybrid systems framework. Then, we establish conditions for exponential stability of the polynomial system by employing the observer. Additionally, the designed observer ensures the exponential input-to-state stability for the hybrid error system in the presence of external disturbances. Finally, we provide an illustrative example to demonstrate the validity of the designed observer in estimating the states of the polynomial system and guaranteeing input-to-state stability under external disturbance.