Lyapunov Matrix-Based Guaranteed Cost Dynamic Positioning Control for Unmanned Marine Vehicles with Time Delay*

This paper presents a Lyapunov matrix-based guaranteed cost dynamic positioning controller for unmanned marine vehicles (UMVs) with time delays. A novel Lyapunov-Krasovskii functional (LKF) is introduced, which enhances the analysis of time delays and system states. The controller design leverages the LMI framework alongside Jensen's inequality to determine sufficient criteria for its feasibility, ensuring that the UMV s' state errors gradually reduce to zero and providing an adaptive <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance guarantee. Additionally, the cost function is upperbounded, and the effectiveness of the method is demonstrated through simulation results.