Reachability and Controllability of LTI Systems

This lecture covers the concepts of reachability and controllability of Linear Time-Invariant (LTI) systems. It explains how to test reachability, the properties of unreachable subspaces, and the conditions for a system to be reachable. The lecture also delves into the definitions of reachability, the reachability matrix, and the reachability test. Additionally, it discusses controllability, controllable states, and the relationship between controllability and reachability. The instructor provides examples, proofs, and insights on how to build the reachability matrix and determine controllability. The lecture concludes by exploring whether controllability and reachability coincide and the implications of reversible LTI systems.