# construct 2-state observer

I have position $\theta(s) = \frac{s^2+1}{s^4+2s^3+3s^2+4s+5}$ and velocity $\dot\theta(s) = \frac{s(s^2+1)}{s^4+2s^3+3s^2+4s+5}$.

How do I construct 2-state-observer with sampling time $T_s$?

$\left[ \begin{array}{c} \theta_{k+1}\\ \dot\theta_{k+1}\\ \end{array} \right] =A\left[ \begin{array}{c} \theta_{k}\\ \dot\theta_{k}\\ \end{array} \right]$

• What have you tried so far? Can you build an observer for a simpler system? We need to know your level of understanding the topic before we can help you. – Phonon Oct 15 '13 at 18:08
• You've also only told us half (or less) of the problem. What measurements do you have to observe the state with? What is the driving force for the state update? How noisy are the measurements? – Peter K. Oct 15 '13 at 20:38
• Sorry. I add more information. Measurements is position from linear encoder. $C=\left[ \begin{array}{cc} 1 && 0 \end{array} \right]$ – Kho Oct 15 '13 at 22:02