# 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

collapse all

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.

## 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`.