2. Time-Domain Analysis

Observability — Quiz

Test your understanding of observability with 5 practice questions.

Practice Questions

Question 1

Which of the following describes a system where all initial states can be uniquely determined from the output measurements over a finite time interval?

Question 2

For a linear time-invariant (LTI) system, what is the rank condition for the observability matrix $O$ to ensure observability?

Question 3

If a system is unobservable, what does this imply about the ability to design a state observer?

Question 4

Consider a system with state matrix $A = \begin{pmatrix} 1 & 0 \\ 0 & 2 \end{pmatrix}$ and output matrix $C = \begin{pmatrix} 0 & 1 \end{pmatrix}$. What is the observability matrix for this system?

Question 5

What is the primary purpose of performing an observability test on a control system?