LMIs in Control/pages/Hurwitz detectability

Hurwitz Detectability 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 where , , , at any . The Data The matrices are system matrices of appropriate dimensions and are known. The Optimization Problem 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: Matrix pair , is Hurwitz detectable if and only if following LMI holds Conclusion: Thus by proving the above conditions we prove that the matrix pair is Hurwitz Detectable. Implementation Find the MATLAB implementation at this link below Hurwitz detectability Related LMIs Links to other closely-related LMIs LMI for Hurwitz stability LMI for Schur stability Schur Detectability External Links 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: https://en.wikibooks.org/wiki/LMIs_in_Control