LMIs in Control/pages/Hankel Norm for Affine Parametric Varying Systems
The System[edit | edit source]
where and depend affinely on parameter .
The Data[edit | edit source]
The matrices .
The Optimization Problem:[edit | edit source]
Solve the following semi-definite program
where is the controllability Gramian, i.e., .
Implementation[edit | edit source]
Conclusion[edit | edit source]
The Hanakel norm (i.e., the square root of the maximum eigenvalue) of is less than if and only if the above LMI holds and the value function returns the maximum provable Hankel norm.
Remark[edit | edit source]
is assumed to be zero.
External Links[edit | edit source]
- 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.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.