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




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:





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


  • [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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