# LMIs in Control/pages/Mu Analysis

Mu Synthesis. The technique of synthesis extends the methods of synthesis to design a robust controller for an uncertain plant. You can perform synthesis on plants with parameter uncertainty, dynamic uncertainty, or both using the "musyn" command in MATLAB. analysis is an extremely powerful multivariable technique which has been applied to many problems in the almost every industry including Aerospace, process industry etc.

**The System:**[edit | edit source]

Consider the continuous-time generalized LTI plant with minimal states-space realization

where it is assumed that is Invertible.

**The Data**[edit | edit source]

The matrices needed as inputs are only, and .

**The LMI:** - Analysis[edit | edit source]

The inequality holds if and only if there exist and , where , satisfying:

**Conclusion:**[edit | edit source]

The inequality holds for where X satisfies the above Inequality.

**Implementation**[edit | edit source]

**External links**[edit | edit source]

- [1]-MATLAB -synthesis Implementation
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.