Multivariable Control: Lyapunov Stability and LQR Theorems

This lecture covers the concepts of Lyapunov stability theory, discounted LQR, and the stability theorems related to multivariable control. It explains the importance of observability, the solution of the ARE, and the Schur stability of closed-loop systems. The instructor discusses the use of Lyapunov functions, the proof of stability theorems, and the implications of prescribed stability degrees in LQR. Additionally, the lecture explores the discounted LQR problem, the associated cost function, and the algorithm for determining the LQR gain. Various remarks on LQR, stability criteria, and the relationship between modes and eigenvalues are also presented.