Eigenvalue Assignment in Multivariable Control

This lecture covers the proof of Ackermann's formula and examples of eigenvalue assignment for multi-input systems. It explains how to design controllers directly as a function of the system matrices A and B, avoiding the use of coordinates. The lecture also demonstrates the computation of the desired closed-loop characteristic polynomial and the controller matrix K using the Ackermann's formula. Additionally, it presents simplified methods for eigenvalue assignment in MIMO systems, including feedback on a scalar channel and a probabilistic approach. The instructor illustrates these concepts with examples of state-feedback controller design and simulations.