LMIs in Control/pages/Robust stabilization of nonlinear systems

LMIs in Control/pages/Robust stabilization of nonlinear systems

Robust Stabilization of Nonlinear Systems

The Optimization ProblemEdit

Consider 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 DataEdit

The matrices required to solve this problem are A, B, H

The LMI: Nonlinear Systems Robust StabilizationEdit

There exists scalars  ,  , and  , along with the matrices   such that the following optimization problem is feasible.

 

Conclusion:Edit

The controller K can be recovered by the relation

 

ImplementationEdit

External LinksEdit

A list of references documenting and validating the LMI.

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