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

Stabilizability LMI 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. Thus, stabilizability is a essentially a weaker version of the controllability condition. 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 Hurwitz Stability 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: