# LMIs in Control/pages/DCGain

< LMIs in Control | pages

The continuous-time DC gain is the transfer function value at the frequency s = 0.

**The System**Edit

Consider a square continuous time Linear Time invariant system, with the state space realization and

**The Data**Edit

** The LMI: LMI for DC Gain of a Transfer Matrix**Edit

The transfer matrix is given by

The DC Gain of the system is strictly less than if the following LMIs are satisfied.

OR

**Conclusion**Edit

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**

**Implementation**Edit

A link to the Matlab code for a simple implementation of this problem in the Github repository:

** External Links**Edit

- [1] - 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.
- [2] -Mathworks reference to DC Gain