2. Time-Domain Analysis

State-space Review — Quiz

Test your understanding of state-space review with 5 practice questions.

Practice Questions

Question 1

Which of the following transformations is commonly used to convert a continuous-time state-space model into a discrete-time state-space model?

Question 2

Consider a system described by the state-space equations: $ \dot{\mathbf{x}}(t) = \mathbf{A}\mathbf{x}(t) + \mathbf{B}\mathbf{u}(t) $ and $ \mathbf{y}(t) = \mathbf{C}\mathbf{x}(t) + \mathbf{D}\mathbf{u}(t) $. If the system has no direct feedthrough from input to output, which matrix would be a zero matrix?

Question 3

For a linear time-invariant (LTI) system, what condition must the eigenvalues of the system matrix $\mathbf{A}$ satisfy for the system to be asymptotically stable?

Question 4

When analyzing the stability of a discrete-time LTI system described by $ \mathbf{x}[k+1] = \mathbf{A}\mathbf{x}[k] + \mathbf{B}\mathbf{u}[k] $, what condition must the eigenvalues of the system matrix $\mathbf{A}$ satisfy for the system to be asymptotically stable?

Question 5

Which of the following methods is used to determine the state transition matrix $ e^{\mathbf{A}t} $ for a given system matrix $\mathbf{A}$?