The field of control theory and AI resilience is moving towards the development of novel methodologies for ensuring the stability and robustness of complex systems. Researchers are exploring the application of control theory principles to AI systems, such as LSTM networks, to guarantee their resilience against input perturbations. Additionally, there is a focus on the development of dynamic state-feedback controllers for LPV systems, which can ensure exponential stability and optimal performance. The analysis of local stability and region of attraction for nonlinear systems, including those with neural network feedback, is also an active area of research. Furthermore, the comparison of traditional control methods, such as PI control, with nonlinear passivity-based control approaches is highlighting the benefits of the latter in terms of stability and performance. Noteworthy papers in this area include:

• A paper that proposes a novel methodology for guaranteeing the resilience of LSTM networks using control theory principles, which can advance AI applications in control systems.
• A paper that presents a dynamic state-feedback controller for LPV systems, which can ensure exponential stability and optimal performance.
• A paper that develops novel methods for estimating the Region of Attraction for nonlinear systems with neural network feedback, which can improve the analysis and design of such systems.