Stability and Reachability in Multivariable Control

This lecture covers stability analysis of equilibrium states in linear time-invariant (LTI) systems, including Lyapunov stability and asymptotic stability. It also discusses the relationship between stability and the error dynamics of LTI systems. The lecture further explores the concepts of reachability and controllability, highlighting the importance of these properties in determining the system's behavior. Examples are provided to illustrate the application of these concepts in analyzing the stability and controllability of dynamical systems. The lecture concludes with a detailed explanation of the reachability matrix and its role in determining the reachability of a system.