LMIs in Control/pages/DCGain

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

The System[edit | edit source]

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

The Data[edit | edit source]

The LMI: LMI for DC Gain of a Transfer Matrix[edit | edit source]

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


Conclusion[edit | edit source]

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 | edit source]

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


External Links[edit | edit source]