LMIs in Control/Click here to continue/Controller synthesis/Controller to achieve the desired Reachable set; Polytopic uncertainty

Reachable sets with unit-energy inputs; Polytopic uncertainty edit

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 System edit

 

Where:

 

In case of polytopic uncertainty, we have:

 

Reachable set edit

The reachable set can be defined:

 

The elipsoid   contains  

The Data edit

The matrices  . And

The Optimization Problem edit

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 Links edit

A list of references documenting and validating the LMI.


Return to Main Page: edit