# Documentation

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# pzmap

Pole-zero plot of dynamic system

## Syntax

pzmap(sys)pzmap(sys1,sys2,...,sysN)[p,z] = pzmap(sys)

## Description

pzmap(sys) creates a pole-zero plot of the continuous- or discrete-time dynamic system model sys. For SISO systems, pzmap plots the transfer function poles and zeros. For MIMO systems, it plots the system poles and transmission zeros. The poles are plotted as x's and the zeros are plotted as o's.

pzmap(sys1,sys2,...,sysN) creates the pole-zero plot of multiple models on a single figure. The models can have different numbers of inputs and outputs and can be a mix of continuous and discrete systems.

[p,z] = pzmap(sys) returns the system poles and (transmission) zeros in the column vectors p and z. No plot is drawn on the screen.

You can use the functions sgrid or zgrid to plot lines of constant damping ratio and natural frequency in the s- or z-plane.

## Examples

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Plot the poles and zeros of the continuous-time system represented by the following transfer function:

 
H = tf([2 5 1],[1 3 5]); pzmap(H) grid on 

Turning on the grid displays lines of constant damping ratio (zeta) and lines of constant natural frequency (wn). This system has two real zeros, marked by o on the plot. The system also has a pair of complex poles, marked by x.

Plot the pole-zero map of a discrete time identified state-space (idss) model. In practice you can obtain an idss model by estimation based on input-output measurements of a system. For this example, create one from state-space data.

A = [0.1 0; 0.2 -0.9]; B = [.1 ; 0.1]; C = [10 5]; D = [0]; sys = idss(A,B,C,D,'Ts',0.1); 

Examine the pole-zero map.

pzmap(sys) 

System poles are marked by x, and zeros are marked by o.

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### Tips

• For MIMO models, pzmap shows all system poles and transmission zeros on a single plot. To map poles and zeros for individual I/O pairs, use iopzmap.

• For additional options for customizing the appearance of the pole-zero plot, use pzplot.

### Algorithms

pzmap uses a combination of pole and zero.

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