LMIs in Control/pages/S Procedure

LMIs in Control/pages/S Procedure


S-Procedure

The Optimization ProblemEdit

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 DataEdit

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-ProcedureEdit

There exists a scalar   where:

 

Conclusion:Edit

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.


ImplementationEdit

External LinksEdit

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