Control System Toolbox™

dcgain - Low-frequency (DC) gain of LTI system

Syntax

k = dcgain(sys)

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

The continuous-time DC gain is the transfer function value at the frequency . For state-space models with matrices , this value is

The discrete-time DC gain is the transfer function value at . For state-space models with matrices , this value is

The DC gain is infinite for systems with integrators.

To compute the DC gain of the MIMO transfer function

type

H = [1 tf([1 -1],[1 1 3]) ; tf(1,[1 1]) tf([1 2],[1 -3])]
dcgain(H)
ans =
    1.0000   -0.3333
    1.0000   -0.6667