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LMIs in Control/pages/S Procedure

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LMIs in Control/pages/S Procedure


S-Procedure

The Optimization Problem

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In general procedures, considering following quadratic function , where . The inequality is satisfied when all .


Where , and

This type of procedure is used to help solve problems that were originally NP-hard problems. An example of this is the following inequality: . By using the defined problem above, an LMI can be constructed using the S-Procedure:


Where the scalar .

The Data

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The data is dependent on the type of problem being solved, and is used more as a tool to solve complex problems that were difficult to solve before.

The LMI: S-Procedure

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There exists a scalar where:

Conclusion:

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The results from this LMI will help construct quadratic stability as quadratic stability requires matrix positivity on a subset. Examples of this implementation include creating a controller based on parametric, norm-bounded uncertainties for robust problems.


Implementation

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