Linear Systems: Equilibria and Stability

This lecture covers the basic properties of linear systems, equilibria, stability, and modes of a linear system. It explains the superposition principle, Lagrange formula, equilibria of LTI systems, and stability analysis of equilibria. The instructor discusses equivalent LTI systems, stability definitions, Lyapunov stability, and exponential stability. The lecture also reviews the analysis of free states and the characterization of modes associated with distinct eigenvalues. Various theorems and remarks are presented to aid in understanding the stability of linear systems.