Observer-Based Target Control for Mismatched Time-Delay Systems

This paper addresses observer-based target control for linear time-delay systems subject to simultaneous, mismatched input and output latencies. While full-state regulation is often conservative and computationally intensive, practical engineering objectives typically require controlling only specific linear combinations of states, or target outputs. To overcome the challenges posed by these asymmetric, dual-channel delays, we propose a reduced-order modeling framework inspired by the structural philosophy of Fernando and Darouach \cite{Fernando2025}. By projecting the high-dimensional plant dynamics onto the row space of the target output matrix $F_o$, the controller focuses strictly on the lower-dimensional target subspace. Based on this projection, an observer-based control scheme is developed to ensure precise target stabilization despite the simultaneous, mismatched input, state, and output latencies.