A robust prediction-based H-infinity control strategy forneutral-type time-delay systems with input delay

State prediction is a widely used approach to compensate for input delays incontrol systems; however, its accuracy is inherently dependent on the modeldynamics, making prediction errors unavoidable. Such errors can cause deviations in the applied control commands, leading to performance degradation andpotential system instability. In this study, a robust prediction-based H-infinity control strategy is proposed for Neutral-type Delay Differential Equations (NDDEs) with state and input time delays. The unmodeled dynamics are represented asan exogenous input, which not only directly impacts control performance but also introduces state prediction errors, further a ecting control effort. To address these challenges, the control gains are optimally tuned to minimize the H-infinity norm of the transfer function between the exogenous input and the system output, ensuring robustness against disturbances. A practical example of time-delay systems, i.e., the oil-well drill-string system, is employed to demonstrate the effectiveness of the proposed controller. Specifically, the H-infinity controller is applied to a coupled axial-torsional model of a drill-string, formulated as an NDDE with both state and input delays. Simulation results highlight the superior performance ofthe designed controller in mitigating disturbances and optimizing control gainsto achieve minimal H-infinity norm.