Controllability and Observability

This lecture covers the concepts of controllability and observability in linear systems. It starts by defining controllability as the ability to transfer the system from any initial state to any final state in finite time with an appropriate input. The lecture then discusses the necessary and sufficient conditions for controllability, including the controllability matrix and the controllability Gramian. It also explores the implications of unimodular matrices on the solution space and the importance of the controllability and observability matrices in system analysis.