LMIs in Control/pages/DCGain

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

The SystemEdit

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

 

The DataEdit

 

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.

  


OR

  

ConclusionEdit

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

ImplementationEdit

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

https://github.com/yashgvd/LMI_wikibooks

External LinksEdit