H∞ State-Observer Controller Synthesis for Multiple Time-Delay Systems

In order to achieve the desired operational state using a state feedback controller for nonfully measured states, it is necessary for the controller to possess information regarding all states. The unmeasured states are estimators and inputs to the controller. This article aims to provide a synthesis of the controller and observer, ensuring closed-loop stability and fulfilling performance requirements in the presence of disturbances. The closed loop asymptotic stability of multiple state delayed systems can be ensured by a sufficient condition stated in a linear matrix inequality (LMI). This condition satisfies the H
∞
norm bound constraint. The proposed technique is demonstrated numerically to design observer-based controllers for commonly used dynamic models in literature. The simulation results demonstrates that the controllers have the capability to drive the states towards the origin.