While the dissipativity-based approach offers formal guarantees of closed-loop stability and performance, it may have limitations compared to other stability or performance certification methods for neural network controllers. One limitation is the conservative nature of dissipativity analysis, which may lead to overly restrictive controller designs. Additionally, the computational complexity of solving the matrix inequalities for dissipativity certification can be high, especially for large-scale systems or complex neural network architectures. Furthermore, the dissipativity-based approach may not provide insights into the transient behavior or robustness of the controller, which are important aspects in practical control applications.