When applying the proposed observer design methodology to real-world systems, there are several potential challenges and limitations that need to be considered. One challenge is the computational complexity involved in solving the LMI optimization problems, especially for systems with high-dimensional state spaces or complex nonlinearities. This can lead to longer computation times and increased computational resources. To address this, efficient numerical algorithms and optimization techniques can be employed to streamline the computation process and improve the scalability of the method.
Another limitation is the reliance on accurate system models and parameter estimates, which may not always be available in practical applications. Uncertainties in the system dynamics or disturbances can affect the performance of the observer and lead to suboptimal results. To mitigate this, robust observer design techniques, such as H-infinity control or adaptive observers, can be integrated into the methodology to enhance the system's resilience to uncertainties and disturbances.
Furthermore, the implementation of the observer design on hardware platforms may pose challenges in terms of real-time processing, sensor integration, and communication with the control system. Ensuring the seamless integration of the observer into the overall control architecture and addressing any hardware constraints are essential for successful deployment in real-world systems.