Memory and Memoryless Composite H-infinity State Feedback Control for Linear Time-Delay Systems

In this paper, we revised the simulation example from the original work "Memory and Memoryless Composite H-infinity State Feedback Control for Linear Time-Delay Systems." Our analysis revealed that the original example had no feasible solution based on Theorem 1. Additionally, we conducted simulation verification using MATLAB's Linear Matrix Inequality (LMI) toolbox, implementing the control algorithm through functions like lmivar for variable definition and feasp for solving LMI constraints.

Specifically, we reconstructed the simulation model and performed a series of simulation experiments to better understand the performance of this control method. The implementation involved defining system matrices with time-delay components, formulating H-infinity constraints as LMIs, and solving the optimization problem using MATLAB's LMI solver. We observed that this method demonstrates excellent performance in controlling linear time-delay systems, effectively maintaining system stability and performance metrics. Through our simulations, we verified that the method not only reduces system settling time but also minimizes steady-state error, thereby enhancing overall system performance.

Furthermore, we conducted an in-depth analysis of the method's advantages and limitations, proposing potential improvements for future research. We believe that with further refinement and investigation, this control strategy could find significant applications across broader engineering domains.