# 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

### Example 1

Pole-Zero Plot of Dynamic System

Plot the poles and zeros of the continuous-time system

$H\left(s\right)=\frac{2{s}^{2}+5s+1}{{s}^{2}+2s+3}$

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

### Example 2

Plot the `pzmap` for a 2-input-output discrete-time IDSS model.

```A = [0.1 0; 0.2 0.9]; B = [.1 .2; 0.1 .02]; C = [10 20; 2 -5]; D = [1 2; 0 1]; sys = idss(A,B,C,D, 'Ts', 0.1);```

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### Tips

You can change the properties of your plot, for example the units. For information on the ways to change properties of your plots, see Ways to Customize Plots.

### Algorithms

`pzmap` uses a combination of `pole` and `zero`.