Lyapunov Methods: Stability Analysis

This lecture covers the analysis of nonlinear control systems using Lyapunov methods, focusing on Lyapunov functions, stability definitions, and equivalence with linear systems. It also discusses the concept of stability at equilibrium points and the criteria for stability. The lecture delves into formal definitions of stability, viability, and stability candidates by Lyapunov, emphasizing the importance of Lyapunov functions in determining system stability. Additionally, it explores the relationship between mechanical analogies and stability definitions, highlighting the role of energy concepts in stability analysis. The lecture concludes with a detailed examination of Lyapunov stability candidates and their significance in ensuring system stability.