Global Asymptotic Stability

Global asymptotic stability, a key concept in dynamical systems, focuses on determining whether a system's trajectories converge to a single equilibrium point regardless of the initial conditions. Current research emphasizes developing and analyzing algorithms and models, including recurrent neural networks, Takagi-Sugeno fuzzy systems, and physics-informed neural networks, to ensure or verify this stability, often within specific contexts like optimization or control systems. These investigations are crucial for designing robust and reliable systems across diverse applications, from robotics and process control to machine learning and artificial intelligence, where stability guarantees are essential for safe and predictable operation. The development of less conservative stability conditions and efficient computational methods remains a central theme.