Fundamental System Properties

Determine the stability of a system by analyzing the eigenvalues of the state matrix.

Define controllability and explain its physical interpretation in the context of state control.

Compute the controllability matrix and use its rank to determine if a system is controllable.

Define observability and explain its physical interpretation in the context of state estimation.

Compute the observability matrix and use its rank to determine if a system is observable.

Relate uncontrollable or unobservable modes to pole-zero cancellations in a system's transfer function.