# What does an eigenvalue tell us about the system?

I have an electrical system to be controlled (Cuk converter). So I get the space-state model given by: $$\dot{x}(t)=Ax(t)+Bu(t)$$

If I determine the eigenvalues (of the matrix A) I obtain: $${-113.654 + 482.816 j, -113.654 - 482.816 j, -85.204 + 174.817 j, -85.204 - 174.817 j}$$ with $j$ as the imaginary unit.

So, can I tell something about the system from these eigenvalues? Like, can I predict the order of the unit-response or impulse response? Does it mean something that the eigenvalues are complex and conjugated?

• A switching regulator has numerous (small) energy storage mechanisms; all these parasitics implement a very high order system; avoiding chaotic behavior becomes your task. I've seen PhDs in SwitchReg not be able to develop a cleanly operating SwitchReg. Beware of the many parasitics. – analogsystemsrf Sep 7 '17 at 17:12

## 1 Answer

The eigenvalues are the poles of the system. The number of eigenvalues is the order of the system. Complex conjugate poles will contribute oscillations to the response.

• And conjugated poles mean an oscillating response. – next-hack Sep 7 '17 at 14:29
• Are they ALWAYS the poles of the system? As far as I know, there were a condition about it. If the system satisfies X condition, then the eigenvalues are the poles but I'm not sure, I did read it a time ago.. – Miguel Duran Diaz Sep 7 '17 at 14:31
• All dynamic systems have poles. – PICyPICyPICy Sep 7 '17 at 14:53
• You may wanna check this link math.stackexchange.com/questions/866939/… in which eigenvalues versus poles is discussed. By the way, what don't use the PWM switch model to analyze the Cùk converter? – Verbal Kint Sep 7 '17 at 15:00