Observer Design for Networked Linear Systems with Fast and Slow Dynamics under Measurement Noise

This paper addresses the emulation-based observer design for networked control systems (NCS) with linear plants that operate at two time scales in the presence of measurement noise. The system is formulated as a hybrid singularly perturbed dynamical system, enabling the systematic use of singular perturbation techniques to derive explicit bounds on the maximum allowable transmission intervals (MATI) for both fast and slow communication channels. Under the resulting conditions, the proposed observer guarantees that the estimation error satisfies a global exponential derivative-input-to-state stability (DISS)-like property, where the ultimate bound scales proportionally with the magnitudes of the measurement noise and the time derivative of the control input. The effectiveness of the approach is illustrated through a numerical example.