LMIs in Control/pages/S Procedure

S-Procedure The Optimization Problem 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 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 There exists a scalar where: Conclusion: 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 S-Procedure Example External Links LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet. LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes. LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd. Return to Main Page: