Trinh et al. solve mismatched input-output delay control

A new paper on arXiv (2606.03081) by Hieu Trinh, Phan Thanh Nam, and Tran Ngoc Nguyen tackles a persistent challenge in control theory: stabilizing linear systems that suffer from simultaneous, independently varying delays in control input and system output. Unlike prior work that often assumes matched delays or requires restrictive conditions, this framework handles mismatched delays where the output measurement delay τ_y is completely independent of the input delay τ_u. The proposed solution unfolds in two stages. First, an asymptotically stabilizing delayed state-feedback controller is synthesized using recent Linear Matrix Inequality (LMI) techniques. Second, the controller is realized via novel time-delay compensators, allowing the control law to be estimated directly from delayed output measurements.

This architecture is more than a theoretical exercise—it directly addresses real-world scenarios such as networked control systems, teleoperation, and remote manufacturing where communication lags in different paths (sensor vs. actuator) are unrelated. The authors also extend their method to target output controllers, broadening applicability to systems where only partial state information is available. With MSC classifications spanning delay differential equations, control synthesis, and robust stability, the work bridges gaps between LMI-based design and practical delay compensation. For engineers and researchers, this offers a mathematically rigorous yet implementable path to stabilizing plants with independent input-output delays, a problem that has long resisted simple solutions.