LMIs in Control/pages/Hurwitz detectability
LMIs in Control/pages/Hurwitz detectability
Hurwitz Detectability[edit | edit source]
Hurwitz detectability is a dual concept of Hurwitz stabilizability and is defined as the matrix pair , is said to be Hurwitz detectable if there exists a real matrix such that is Hurwitz stable.
The System[edit | edit source]
where , , , at any .
The Data[edit | edit source]
- The matrices are system matrices of appropriate dimensions and are known.
The Optimization Problem[edit | edit source]
There exist a symmetric positive definite matrix and a matrix satisfying
There exists a symmetric positive definite matrix satisfying
with being the right orthogonal complement of .
There exists a symmetric positive definite matrix such that
for some scalar
The LMI:[edit | edit source]
Matrix pair , is Hurwitz detectable if and only if following LMI holds
Conclusion:[edit | edit source]
Thus by proving the above conditions we prove that the matrix pair is Hurwitz Detectable.
Implementation[edit | edit source]
Find the MATLAB implementation at this link below
Hurwitz detectability
Related LMIs[edit | edit source]
Links to other closely-related LMIs
LMI for Hurwitz stability
LMI for Schur stability
Schur Detectability
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.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.