Multivariable Control: State-Feedback and Eigenvalue Assignment

This lecture covers the design of state-feedback controllers for multivariable systems, focusing on the Eigenvalue Assignment problem. The instructor explains the canonical controllability form, the reachability matrix, and the solution to the Eigenvalue Assignment problem for single-input systems. The lecture also discusses the Ackermann's formula for controller design and presents simplified methods for MIMO systems, including feedback on a scalar channel and a probabilistic approach. The drawbacks of these methods are highlighted, emphasizing the limitations of using only a single input or making random choices for feedback gain.