Module 3 : Stability analysis of discrete time systems

Lecture 1 : Stability Analysis of closed loop system in z-plane

1.1 Jury Stability Test

Assume that the characteristic equation is as follows,

$ P(z)=a_{0}z^{n}+a_{1}z^{n-1}+...+a_{n-1}z+a_{n}$ , where $ a_{0}>0$.

Jury Table
  $\displaystyle Row$ $\displaystyle \quad z^{0} \quad z^{1} \quad z^{2}\quad z^{3}\quad z^{4} \quad ...\quad z^{n}$  
  1 $\displaystyle \quad a_{n} \quad a_{n-1} \quad a_{n-2} ... \quad...\quad...\quad a_{0}$  
  2 $\displaystyle \quad a_{0} \quad a_{1} \quad a_{2} ...\quad...\quad...\quad... \quad a_{n}$  
  3 $\displaystyle \quad b_{n-1} \quad b_{n-2} \quad ...\quad ...\quad b_{0}$  
  4 $\displaystyle \quad b_{0} \quad b_{1} \quad ...\quad ...\quad ...\quad b_{n-1}$  
  5 $\displaystyle \quad c_{n-2} \quad c_{n-3} ...\quad c_{0}$  
  6 $\displaystyle \quad c_{0} \quad c_{1} ... \quad ...\quad c_{n-2}$  
  . $\displaystyle \quad............................$  
  . $\displaystyle \quad............................$  
  . $\displaystyle \quad............................$  
  $\displaystyle 2n-3$ $\displaystyle \quad q_{2} \quad q_{1} \quad q_{0}$  

where,


This system will be stable if: