LMIs in Control/Stability Analysis/Stabilizability LMI

Stabilizability LMI Stabilizability is a essentially a weaker version of the controllability condition. A system is stabilizable if all unstable modes of the system are controllable. This implies that if the system is controllable, it will also be stabilizable. The LMI condition for stabilizability of 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 A. The LMI: Stabilizability LMI is stabilizable if and only if there exists such that , where the stabilizing controller is given by . Conclusion: If we are able to find such that the above LMI holds it means the matrix pair is stabilizable. In words, a system pair is stabilizable if for any initial state an appropriate input can be found so that the state asymptotically approaches the origin. Stabilizability is a weaker condition than controllability in that we only need to approach as whereas controllability requires that the state must reach the origin in a finite time. Implementation This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/Stabilizability_LMI.m Related LMIs WIP: Will be linked once they have been created. Controllability LMI Hurwitz Stability LMI Schur Stability LMI Observability LMI Detectability 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: