Inputs

sys

LTI system created by tf(), ss(), dss(), etc.

Outputs

K

DC gain matrix. For a system with m inputs and p outputs, the array k has dimensions [p, m].

See @lti/dcgain for the method used for systems not represented by a transfer function.

For a continuous-time system G(s) of the form $$ G(s) = \frac{b_ns^n + \cdots + b_1s+ b_0}{a_ns^n + \cdots + a_1s+ a_0} $$ the gain is given by $$ K = G(s=0) = \frac{b_0}{a_0} $$

In the discrete-time case the gain of $$ G(z) = \frac{b_nz^n + \cdots + b_1z+ b_0}{a_nz^n + \cdots + a_1z+ a_0} $$ is given by $$ K = G(z=1) = \frac{\sum_{i=0}^n b_i}{\sum_{i=0}^n a_i} $$

Example

 G = tf ({[1 0],[1 1]},{[1 1],[1,0]});
 K = dcgain (G)
 K =
   0  Inf

See also: @lti/dcgain, @lti/freqresp, @tf/tf, @ss/ss, dss

Source Code: @tf/dcgain