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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

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

The Data

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The LMI: LMI for DC Gain of a Transfer Matrix

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


OR

Conclusion

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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

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

https://github.com/yashgvd/LMI_wikibooks

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