Lyapunov Stability in Dynamical Systems

This lecture discusses Lyapunov stability, a crucial concept in dynamical system analysis and control system design. It covers the definition of equilibrium points, global asymptotic stability, and the role of Lyapunov functions. The lecture explores methods to assert stability properties using Lyapunov's stability theory, focusing on global asymptotic stability. It also delves into the application of stability theory in scenarios like drone trajectory tracking. The lecture concludes with a practical implementation of stability analysis through semidefinite programming and numerical simulations.