1. Fundamentals

System Properties — Quiz

Test your understanding of system properties with 5 practice questions.

Practice Questions

Question 1

For a linear time-invariant (LTI) system, if the system matrix $\mathbf{A}$ has an eigenvalue with a positive real part, what can be concluded about the system's stability?

Question 2

Consider a system described by the state-space equations: $\dot{x} = Ax + Bu$ $\text{y} = Cx$ If the system is completely controllable, what does this imply about the controllability matrix $\mathcal{C}$?

Question 3

What is the primary implication if a system's observability matrix does not have full row rank?

Question 4

A system is considered realizable if its input-output behavior can be represented by a finite-dimensional state-space model. Which of the following is a key characteristic of a realizable system?

Question 5

Consider a system with the transfer function $G(s) = \frac{s+2}{s^2 + 5s + 6}$. Determine the stability of the system.