Accumulative-Event-Based Proportional–Integral Observer Design for Partially State-Saturated Systems Under Probabilistic Quantizations

In this article, we address the design issue of the proportional-integral observer (PIO) for partially state-saturated systems, which are affected by probabilistic quantizations and an accumulation-based event-triggered mechanism (ABETM). A comprehensive model is established to characterize partial state saturations, wherein only a part of the state variables are saturated while the remaining variables maintain normal conditions. To conserve communication resources, an ABETM is employed to determine the release of system measurements to the PIO. Before transmission over the communication network, the triggered signal is quantized through a probabilistic quantization mechanism. The goal of this article is to devise a PIO that guarantees ultimate boundedness of the estimation error dynamics in the mean square. Initially, a sufficient condition is derived to ensure that the estimation error dynamics are exponentially ultimately bounded in the mean square. Following this, necessary PIO gains are identified by solving specific matrix inequalities, and the efficacy of this proposed PIO approach is validated using a three-tank system simulation.