# LMIs in Control/pages/Stability of nonlinear systems

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LMIs in Control/pages/Stability of nonlinear systems

**Robust Stability of Nonlinear Systems**

**The Optimization Problem**Edit

Consider a non linear system whos dynamics are given by

where , and , is Hurwitz stable and is piecewise continuous in both and

Assume that

where is the bounding parameter and

**The Data**Edit

The matrices necessary for this LMI are A and H.

**The LMI:** Switched Systems OptimizationEdit

There exists a scalar , along with the matrices such that:

**Conclusion:**Edit

The system is robustly stable to degree is the LMI is feasible.

**Implementation**Edit

**External Links**Edit

A list of references documenting and validating the LMI.

- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- Robust stabilization of nonlinear systems: The LMI approach