LMIs in Control/Click here to continue/LMIs in system and stability Theory/Interval Quadratic Stability
An LMI to determine the quadratic stability of a system with parametric, interval uncertainties.
The System edit
Consider the system with Affine Time-Varying uncertainty
where
where lies in the intervals
where and .
The Data edit
The matrices A and are known.
The Optimization edit
This optimization problem ensures quadratic stability of the system with k interval uncertainties using LMI constraints.
lies in the hypercube. The vertices of the hypercube define the vertices of the uncertainty set
is quadratically stable over if and only if there exists a P > 0 such that
The LMI edit
Conclusion edit
Quadratic Stability Implies Stability of trajectories for any with for all
Quadratic stability is conservative.
Stability does not imply quadratic stability.
Interval uncertainty is a special case of polytopic uncertainty.
Implementation edit
Example of implementation of the LMI
https://github.com/MichaelDobos/LMI/blob/main/intervalquadraticstability.m
Related LMIs edit
External Links edit
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMIs in Control Systems: Analysis, Design, and Applications - A textbook on LMIs in control by Duan and Yu.