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.





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:


External LinksEdit