Stability and Eigenvalues of LTI Systems

This lecture covers stability analysis of Linear Time-Invariant (LTI) systems, focusing on eigenvalues and free states. It explains how stability depends on free states, the relationship between stability and eigenvalues of the system, and the tests for asymptotic stability and instability. The lecture also delves into the concept of simple stability, where all eigenvalues must have modulus less than 1. Additionally, it discusses the reachability and controllability of dynamical systems, emphasizing the possibility of steering states to desired values. The instructor provides examples and definitions to illustrate these concepts, highlighting the importance of reachability in engineering applications.