Duality and PBH Test in Multivariable Control

This lecture covers the concepts of duality and PBH test in multivariable control systems. It starts by explaining the observability matrix and the observability test, followed by the principle of duality and its main properties. The PBH test, which determines the reachability and observability of eigenvalues, is thoroughly discussed with Lemmas and proofs. The lecture also delves into the exact discretization of continuous-time systems, emphasizing the computation of discrete-time dynamics and the state transition operator. Popular discretization methods and the implications of uniform sampling on system dynamics are explored in detail.