Chapter 12, Problem 42P

a.

To determine

The system observability matrix $O_{Mz}$ and show that the system is observable.

b.

To determine

The original system characteristic equation and its observable canonical representation.

c.

To determine

The observable canonical system observability matrix $O_{Mx}$ and its transformation matrix $P=O_{Mz}{}^{-1}{O}_{MX}$ .

d.

To determine

The observer gain matrix $L_x={\left[\begin{array}{cccc}{l}_{1x}& l_{2x}& l_{3x}& l_{4x}\end{array}\right]}^T$

e.

To determine

The corresponding observer gain matrix as $L_z=P{L}_X$ .