Question

A linear system is equivalently represented by two sets of state equations.
$X=AX+BU$ and $W=CW+DU$
The eigen values of the representations are also computed as $\left[\lambda \right]$ and $\left[\mu \right]$. Which one of the following statements is true ?

• A. $\left[\lambda \right]=\left[\mu \right]$ and $X=W$
• B. $\left[\lambda \right]=\left[\mu \right]$ and $X\ne W$
• C. $\left[\lambda \right]\ne \left[\mu \right]$ and $X=W$
• D. $\left[\lambda \right]\ne \left[\mu \right]$ and $X\ne W$

Answer 1

The correct option is B $\left[\lambda \right]=\left[\mu \right]$ and $X\ne W$

Eigen values of $A=\left[\lambda \right]$
Eigen values of $W=\left[\mu \right]$
The eigen values of a system are always unique.
So . $\left[\lambda \right]=\left[\mu \right]$
But a system can be represented by different state models having different set of state variables.
$X=W$
$X\ne W$
Both are possible condtions