LMIs in Control/pages/Reachable set polytopic

Reachable sets with unit-energy inputs; Polytopic uncertaintyEdit

A Reachable set is a set of system States reached under the condition  . On this page we will look at the problem of finding an controller  , that   contains   - reachable set.

The SystemEdit

 

Where:

 

In case of polytopic uncertainty, we have:

 

Reachable setEdit

The reachable set can be defined:

 

The elipsoid   contains  

The DataEdit

The matrices  . And

The Optimization ProblemEdit

The following optimization problem should be solved:

 

Conclusion:Edit

This LMI allows us to investigate stability for the robust control problem in the case of polytopic uncertainty and gives on the controller for this case

Implementation:Edit

  • [1] - Matlab implementation using the YALMIP framework and Mosek solver

Related LMIs:Edit

External LinksEdit

A list of references documenting and validating the LMI.


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