Observer based controller to stabilize linear systems delays

In this paper, an observer-based functional controllers to stabilize delayed linear systems is designed. Delays, whether constant or variable, are a major challenge for the stability of dynamic systems, they generate oscillations and divergence. To overcome these challenges, Linear Matrix Inequality-based methods is used for the design of robust observers capable of compensating for the effects of delays. This problem-based approach is illustrated by numerical examples, which highlight the effectiveness of the presented approach.