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# dcgain

Low-frequency (DC) gain of LTI system

k = dcgain(sys)

## Description

k = dcgain(sys) computes the DC gain k of the LTI model sys.

### Continuous Time

The continuous-time DC gain is the transfer function value at the frequency s = 0. For state-space models with matrices (ABCD), this value is

K = D – CA–1B

### Discrete Time

The discrete-time DC gain is the transfer function value at z = 1. For state-space models with matrices (ABCD), this value is

K = D + C (I – A)–1B

## Examples

### Example 1

To compute the DC gain of the MIMO transfer function

$H\left(s\right)=\left[\begin{array}{cc}1& \frac{s-1}{{s}^{2}+s+3}\\ \frac{1}{s+1}& \frac{s+2}{s-3}\end{array}\right]$

type

```H = [1 tf([1 -1],[1 1 3]) ; tf(1,[1 1]) tf([1 2],[1 -3])];
dcgain(H)
```

to get the result:

```ans =
1.0000   -0.3333
1.0000   -0.6667
```

### Example 2

To compute the DC gain of an identified process model, type;

```load iddata1
sys = idproc('p1d');
syse = procest(z1, sys)

dcgain(syse)
```

The DC gain is stored same as syse.Kp.