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LMIs in Control/pages/Stability of nonlinear systems
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Robust Stability of Nonlinear Systems
The Optimization Problem
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
The matrices necessary for this LMI are A and H.
The LMI: Switched Systems Optimization
There exists a scalar , along with the matrices such that:
Conclusion:
The system is robustly stable to degree is the LMI is feasible.
Implementation
External Links
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
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