Diagonalization

The stability of a linear time-invariant (LTI) system depends on:

• System matrix rank
  

• Input signal

• Eigenvalues of system matrix

• System gain

If all eigenvalues of matrix A have negative real parts, the system is

• Unstable

• Marginally stable

• Asymptotically stable

• Critically damped

A matrix A is diagonalizable if:

• It has at least one eigenvalue
  B. It has real entries
  C. It has n linearly independent eigenvectors
  D. It is symmetric

• It has real entries

• It has n linearly independent eigen vectors

• It is symmetric

In control systems, diagonalization is mainly used to:

• Increase speed of computation

• Simplify controller hardware

• Analyze system dynamics and stability

• Increase system gain

Which tool is commonly used to perform matrix diagonalization in simulations?

• ORCAD
  

• MATLAB

• . AutoCAD

• LabVIEW

For the system x˙=Ax, if matrix A is diagonal, then:

• The system is nonlinear
  

• States are coupled

• Each state evolves independently

• Eigenvalues cannot be found

The characteristic equation of a matrix A is given by:

• 
• 
• 
• 

• Eigenvectors

• Zeros

• Eigenvalues

• Poles

• Nonlinear systems
  

• Systems with repeated poles

• Linear systems with full rank

• Uncontrollable systems

• Eigenvalues
  

• Eigenvectors

• Jordan vectors

• Control gains