Function File: k = dcgain (sys)

Compute the DC gain of LTI system.

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].

Transfer function for a continuous state space system (A,B,C,D) G(s) = C * inv(s*I - A) * B + D

DC Gain: evaluate G(s) as s -> 0: k = C * inv(-A) * B + D

Transfer function for a discrete state space system (A,B,C,D,T) G(z) = C * inv(z*I - A) * B + D

DC Gain: evaluate G(z) as z -> 1: k = C * inv(I-A) * B + D

Example

G = Transfer function 'G' from input 'u1' to output ...

               1          
y1:  ---------------------
     s^3 + 2 s^2 + 3 s + 4


octave:1> K = dcgain(G)

K =  0.25000

See also: freqresp,tf,ss,dss.

Package: control