LMIs in Control/Click here to continue/Observer synthesis/Full-order Hinf state Observer

In this section, we design full order H- state observer. The System Given a state-space representation of a linear system are the state vector, measured output vector and output vectors of interest. are the disturbance vector and control vector respectively. The Data are system matrices Definition For the system , a full order state observer of the form of equation (1) is introduced and the estimate of interested output is given by . : 1 The estimate of interested output is : 2 Given the system and a positive scalar , L is found such that : 3 LMI Condition The state observers problem has a solution if and only if there exists a symmetric positive definite matrix and a matrix satisfying the below LMI : 4 When such a pair of matrics is found, the solution is : 5 Implementation This implementation requires Yalmip and Mosek. https://github.com/ShenoyVaradaraya/LMI--master/blob/main/hinf_obs.m Conclusion Thus, an state observer is designed such that the output vectors of interest are accurately estimated. External Links LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet. 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 & Francis Group, 2013