Robust $H\infty$ Model Reference Tracking Control of Switched Time-Delay Systems with External Disturbances

This paper investigates robust <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H\infty$</tex> model reference tracking control for switched time-delay systems with external disturbances. To address common uncertainties in parameters, external perturbations, and delay issues in practical engineering, a model reference tracking control framework integrating performance metrics is proposed. This framework enables the closed-loop system to achieve state tracking of a reference model while managing switching control in the presence of delays. First, the average dwell time technique is employed to derive the stability of switched time-delay systems and simplify the design of the controller. Then, by utilizing Lyapunov-Krasovskii functional and robust <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H\infty$</tex> model reference tracking control technique, sufficient conditions are proposed to obtain the gains of the robust tracking feedback controller from solvable inequalities and ensure the global exponential stability of the switched time-delay system under external disturbances and actuator faults. Finally, a numerical simulation demonstrates that the proposed method significantly improves disturbance rejection and tracking accuracy.