LMIs in Control/pages/Reachable set normbounded
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Reachable sets with unit-energy inputs; norm bound 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 - reachable set.
The System edit
Where:
In case of norm-bound uncertainty, we have:
The Data edit
The matrices .
.
Reachable set edit
The reachable set can be defined:
The elipsoid
The Optimization Problem edit
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 Links edit
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.