LMIs in Control/pages/Reachable set normbounded

Reachable sets with unit-energy inputs; norm bound 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   - reachable set.

The SystemEdit

 

Where:

 

In case of norm-bound uncertainty, we have:

 

The DataEdit

The matrices  .

 .

Reachable setEdit

The reachable set can be defined:

 

The elipsoid  


The Optimization ProblemEdit

The following optimization problem should be solved:

 

Or

 

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.


Return to Main PageEdit