LMIs in Control/pages/Hurwitz detectability

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LMIs in Control/pages/Hurwitz detectability

Hurwitz Detectability[edit]

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]

where , , , at any .

The Data[edit]

  • The matrices are system matrices of appropriate dimensions and are known.

The Optimization Problem[edit]

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]

Matrix pair , is Hurwitz detectable if and only if following LMI holds


Thus by proving the above conditions we prove that the matrix pair is Hurwitz Detectable.


Find the MATLAB implementation at this link below
Hurwitz detectability

Related LMIs[edit]

Links to other closely-related LMIs
LMI for Hurwitz stability
LMI for Schur stability
Schur Detectability

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.
  • LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.

Return to Main Page:[edit]