LMIs in Control/pages/Output Energy Bounds for Lure System

The System

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The Data

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The matrices  .

The Optimization Problem:

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The following optimization problem should be to find the tightest upper bound for the output energy of the above Lur'e system.

 

Implementation

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https://github.com/mkhajenejad/Mohammad-Khajenejad/blob/master/LMIs%20for%20Output%20Energy%20Bounds%20of%20Lure's%20Systems

Conclusion

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The value function returns the the lowest bound for the energy function of the Lure's systems, i.e.,   with initial conditions  .

Remark

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The key step in the proof is to satisfy  , where   is Lyapunov function in a special form.

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