LMIs in Control/Click here to continue/LMIs in system and stability Theory/Continuous-time Detectability

Detectability LMI Detectability is a weaker version of observability. A system is detectable if all unstable modes of the system are observable, whereas observability requires all modes to be observable. This implies that if a system is observable it will also be detectable. The LMI condition to determine detectability of the pair is shown below. The System where , , at any . The Data The matrices necessary for this LMI are and . There is no restriction on the stability of . The LMI: Detectability LMI is detectable if and only if there exists such that . Conclusion: If we are able to find such that the above LMI holds it means the matrix pair is detectable. In words, a system pair is detectable if the unobservable states asymptotically approach the origin. This is a weaker condition than observability since observability requires that all initial states must be able to be uniquely determined in a finite time interval given knowledge of the input and output . Implementation This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/Detectability_LMI.m Related LMIs Stabilizability LMI Hurwitz Stability LMI Controllability Grammian LMI Observability Grammian LMI 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. LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & amp; Francis Group, 2013, Section 6.1.1 and Table 6.1 pp. 166–170, 192. A Course in Robust Control Theory: a Convex Approach, - by Geir E. Dullerud and Fernando G. Paganini, Springer, 2011, Section 2.2.3, pp. 71-73. Return to Main Page: