LMIs in Control/pages/Robust stabilization of nonlinear systems
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LMIs in Control/pages/Robust stabilization of nonlinear systems
Robust Stabilization of Nonlinear Systems
The Optimization Problem
editConsider a non linear system whos dynamics are given by
where , , and , is Hurwitz stable and is piecewise continuous in both and
We assume is stabilizable so
,
Assume that
where is the bounding parameter and
The Data
editThe matrices required to solve this problem are A, B, H
The LMI: Nonlinear Systems Robust Stabilization
editThere exists scalars , , and , along with the matrices such that the following optimization problem is feasible.
Conclusion:
editThe controller K can be recovered by the relation
Implementation
editExternal Links
editA 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