LMIs in Control/pages/Reachable set polytopic
Reachable sets with unit-energy inputs; Polytopic uncertainty[edit | edit source]
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 | edit source]
In case of polytopic uncertainty, we have:
Reachable set[edit | edit source]
The reachable set can be defined:
The elipsoid contains
The Data[edit | edit source]
The matrices . And
The Optimization Problem[edit | edit source]
The following optimization problem should be solved:
Conclusion:[edit | edit source]
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 | edit source]
-  - Matlab implementation using the YALMIP framework and Mosek solver
Related LMIs:[edit | edit source]
- Reachable sets with unit-energy inputs; Norm-bound uncertainty
- Reachable sets with unit-energy inputs; Diagonal Norm-bound uncertainty
- Quadratic polytopic stabilization
External Links[edit | edit source]
A list of references documenting and validating the LMI.
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes. (3.20.2 page 64)
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.