The continuous-time DC gain is the transfer function value at the frequency s = 0.
Consider a square continuous time Linear Time invariant system, with the state space realization and
The LMI: LMI for DC Gain of a Transfer MatrixEdit
The transfer matrix is given by
The DC Gain of the system is strictly less than if the following LMIs are satisfied.
The DC Gain of the continuous-time LTI system, whose state space realization
is give by ( ), is
- Upon implementation we can see that the value of obtained from the LMI approach and the value of obtained from the above formula are the same
A link to the Matlab code for a simple implementation of this problem in the Github repository:
-  - LMI in Control Systems Analysis, Design and Applications
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
-  -Mathworks reference to DC Gain