Module 7 : Discrete State Space Models

Lecture 2 : State Space Model to Transfer Function

where

2.2 Observable Canonical Form

Equation (3) may be rewritten as

$\displaystyle \left(z^n+\alpha_1z^{n-1}+\ldots+\alpha_n\right)Y(z)=\left(\beta_0z^n+\beta_1z^{n-1}+\ldots+\beta_n\right)U(z)$

$\displaystyle \textrm{or,} \; z^n[Y(z)-\beta_0U(z)]+z^{n-1}[\alpha_1Y(z)-\beta_1U(z)]+\ldots+[\alpha_nY(z)-\beta_nU(z)]=0$

$\displaystyle \textrm{or,} \; Y(z)=\beta_0U(z)+ {z}^{-1}[\alpha_1Y(z)-\beta_1U(z)]+\ldots+z^{-n}[\alpha_nY(z)-\beta_nU(z)]$


The corresponding block diagram is shown in Figure 2.

 

Figure 2: Block Diagram representation of observable canonical form