An Interval Impulsive Observer for Multi-Sensors Linear Systems with Delayed Measurements

This work presents a novel approach to design an interval impulsive observer for a specific class of multi-sensor Linear Time-Invariant system with delayed output measurements with time-varying delays. The observer is located on a remote server and receives sensors data sporadically. The discrete-time delayed measurements are used to design the interval impulsive observer with an open-loop prediction output that helps the observer to catch up the measurement delay. We provide an observer design approach that leverages ${{\mathcal{L}}}_{1}$-gain input/output stability for the delayed observation error dynamics. These stability criteria are a set of algebraic inequalities that are solved via interval analysis. Additionally, we optimize sensor selection by using the predicted reduction of observation error width. An illustrative example is provided to support the theoretical framework, showcasing the practical implications of our approach.