An Improved Equivalent-Input-Disturbance Approach of Disturbances Rejection in Time-Varying State-Delay Systems

This study presents a novel system configuration and design technique to mitigate an external disturbance in a time-varying state-delay system. Within the system’s framework, there exists a plant that serves as an observer, reconstructing its present condition, a more advanced EID estimator that assesses the overall influence of the external disturbance as well as the steady-state element of the fluctuating delay, a controller that utilizes PI to improve the stability of the control system is also included. The stability requirement can be expressed through the utilization of a linear matrix inequality (LMI). The LMI is employed in the creation of the gains for both the PI controller and the state observer. The numerical example serves to illustrate the efficacy of the approach. Furthermore, the method’s validity and superiority are demonstrated by comparing the provided approach with a PI control, an EID-based control, and a traditional PI-EID control system.