LMIs in Control/pages/DCGain

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LMIs in Control/pages/DCGain
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 >0

The Data[edit]

nxn, nxm , pxn , pxm

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.



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 Links[edit]

Return to Main Page:[edit]